"It was always a distraction to me that I had famous parents," says Louise Goffin as we discuss her performance at this weekend's Hyde Park British Summer Time Festival.

She will be appearing alongside her mother, Carole King, Hyde Park's headline act, who is playing her first UK concert in more than 25 years.

The concert is built around King's career-defining 1971 album Tapestry, which sold over 25 million copies worldwide, becoming the first multi-million selling album by a female artist.

"It's amazing to me that 45 years later it resonates so strongly with people," says Goffin of the album. "It speaks to the timelessness of music and stellar songwriting."

Friendly, chatty and enthusiastic, with wavy brown hair and a non-stop smile, Goffin looks a lot like King. And looks aren't all she's inherited. Like her parents she's a songwriter, and like Carole she sings. Goffin tells me that once our interview is over she's going straight into a rehearsal for a performance on Radio Two, where she'll be promoting her eighth and newest album.

She's the daughter of two of the most successful and best-loved singer-songwriters of the twentieth century: King and Gerry Goffin and is well aware of her "amazing legacy".

King, who was born Carole Klein in New York in 1942, met Goffin at Queen's College and the two Jewish songwriters fell into an intense romantic and professional relationship. They married in a Jewish ceremony on Long Island in 1959, when she was 17 and he was 20. Louise was born shortly after, when King was 18 and while the pair were working as songwriters for Aldon Music, which represented the likes of Neil Sedaka and The Shirelles.

It was The Shirelles' version of Will You Love Me Tomorrow? which kick-started the pair's career. It sold over a million records and was the number one song on the Billboard Top 100 charts in 1961 , so Goffin never knew a time when her parents weren't at the top of their musical game.

"I've been recording songs with my parents since I was a child," she says. Her first album was released when she was 19.

Does she go to her mother - a member of the Songwriters Hall of Fame - for advice? Goffin laughs, "I've taught her not to give unsolicited advice!"

"She's an amazing women," Goffin adds. "Empowered, strong, protective of her space. That's something you need to learn as a musician."

Following her stellar career as a songwriter, King broke away to go solo in 1970 with the album Writer. It was her second album, Tapestry, that made her into a household name, at the age of 28.

Explaining why Tapestry became such a phenomenon, King has said: "It came out of the '60s, a tumultuous time with the Vietnam War and the shootings of political figures in 1968, and there was a need for expression of the positive side of people's feelings. Actually, it's not so different from today." And maybe, just one week after the EU referendum shook the UK – and especially the city where the Tapestry concert is being held - it's a prescient time to re-visit the songs.

Goffin admits that until recently she had avoided covering any of her parents' songs.

"I was determined to set out on my own," she says and describes herself as a "born musician; I started writing songs very young and I had too much to say as an artist."

However, on her latest album, The Essential Louise Goffin – Volume 1 which is out later this month, she covers one of King's most famous songs: (You Make Me Feel Like) A Natural Woman, which was written by Gerry Goffin. She has also recorded, but is yet to release, I Feel the Earth Move, from Tapestry, and The Locomotion, written in 1962 by King and Goffin and made a hit by Little Eva, who was Louise's babysitter.

So what changed? In 2011 Goffin was asked to work with her mother on Holiday Carole, King's first studio album in 10 years. Producing that album, she says, made her see how talented and instinctive she was as a musician. "I used to be nervous going into sessions with musicians whose discographies were a mile long, but producing this record, I realised that I knew a lot. They respected me as a 'cat'."

Holiday Carole was nominated for a Grammy and "suddenly my mother was not this big overshadowing presence; it was team work and I was part of the team."

Buoyed up by this experience, she went on to produce her own album, Songs from the Mine - "it felt like it had to be born". However, a month before it was due to come out in 2014, her father died.

"It was not expected," she tells me, visibly moved. In fact she mentions Goffin a number of times during our interview and it is clear they had a very special connection. "I was moved to record one of his songs. It was a tribute to him more or less, that album."

She describes recording songs from the King/Goffin back catalogue as a "natural, organic progression" rather than a "decision to do their songs" that she is now comfortable with. So comfortable in fact that she decided to record Natural Woman, "which, as far as I was concerned: my mother did it, Aretha Franklin did it - thank you very much!

"But I was really pleased with how it came out, my take on it."

Natural Woman is a favourite song of Goffin's, along with Beautiful, which she describes as "an amazing song. It sounds simple but it's written like a Gershwin piece - and I think Carole [Goffin refers to King as 'Carole' when she's talking about her professionally, and 'Mom' in the more personal anecdotes] probably wrote it an about half an hour!"

She refers to the - let's be frank - genius of her parents with a mixture of pride, agreement and heard-it-all-before wryness. When talking about her sons' musical abilities, she describes herself as "in the middle", as if her parents' talents jumped to their grandchildren. But she is far from a forgotten bystander. Her singing voice is as distinctive as her mother's - gentle yet powerful, feminine yet self-assured - but slightly higher pitched. The Essential Louise Goffin has a country-ish feel to it, and she says that in terms of inspiration, "when I hear a really great song it changes me in some way and I deconstruct it." Sitting in her PR's office in St John's Wood, I am treated to what I imagine must be a one-of-its-kind performance.She sings to me the bracha for the lighting of the Chanukah menorah.

As we come to the end of a pretty grim June, the day of the interview is surprisingly sunny and warm, so the song is slightly out of place. Goffin laughs at the juxtaposition. But she hasn't just come out with the song to show off her Jewish credentials to the JC - there is a reason.

She describes her upbringing as "Jewish, and there were definitely Jewish cultures and Yiddish slang, but we were never the family who threw the seder; we just went to it."

"When I was producing the holiday album I didn't want to make just another Christmas record. I thought if I make it a 'holiday' record I can do winter songs."

She says she had grown up hearing her mother sing the "Chanukah prayer and I wanted to do a version of it [on the album] because it's so beautiful."

Then King said: "This has been handed down from my grandmother to my mother, from my mother to me, from me to you – let's make this multi-generational."

So Goffin and her younger son Hayden, who was eight at the time, joined King on the track. Her elder son Elijah - "an incredible musician" - played drums elsewhere on the album.

In her memoir, A Natural Woman, King wrote of this track: "Tears come to my eyes every time I hear the prayer of our ancestors marching forward to future generations through my grandson, my daughter and me."

This idea of being culturally Jewish but not religious has extended to how Goffin has raised her sons. They still light the menorah, albeit to an iPhone recording of King singing the prayer, because Goffin "could never remember the words" - but she says she will "never be a Temple [shul] mom".

"Hayden is an all-or-nothing kinda guy. He said: 'I want my Jewish roots; I want to be barmitzvahed'," Goffin recalls. She was surprised but supportive. "Family is really important to him and he started going to Temple, to Shabbat dinners. I said: 'I want to support you doing this but I am not the mum who will go to Shabbat dinners every Friday night at Temple'."

Laughing as she tells this anecdote, she admits: "I hope your readers don't hate me!"

Talking about Goffin's parenting leads us onto Beautiful: The Carole King Musical, which tells the story of her mother's life and career. After years of success on Broadway it came to London's West End last year and was a runaway success.

When announcing this weekend's concert at Hyde Park earlier in the year, King said that the success of the musical made her realise how large a fan base she had in Britain. "I want to begin by thanking Londoners for making Beautiful so successful," she said. "And now I'm coming to London and can't wait to perform Tapestry from beginning to end for the first time ever! How perfect to be doing that in the heart of one of my favourite cities."

The musical covers Goffin's parents' career - and so their relationship, as the two were so closely interwoven - in stark detail, starting with their young marriage, the birth of Louise and her sister Sherry, and Gerry Goffin's drug addiction and mental health issues, leading to the couple's divorce. What was it like seeing this family history laid bare on stage, to a soundtrack of Up on the Roof, Will You Still Love me? and The Locomotion?

Goffin looks to the side and pauses. Her mother, it is well known, took her time before seeing the show: "She said: 'I lived it, I don't need to see it'." But Goffin took even longer.

"I knew it was very important to my father who had always wanted to write a Broadway show, but [when it previewed] I had really little kids - two and five - so I had my hands full."

When it came to New York however she went with a friend ("I said: 'you have to come with me because I'm going to cry'") and loved it. "It was an amazing experience." She went back with her elder son last year and while she's in London, she's planning on taking her boyfriend to see it here.

Again, she recalls her father. "It was my father's dream and what is really 'beautiful' is that before he died he got to see it in New York. He had no idea how successful it would be. But we have him to thank for that vision."

As the interview comes to an end we come back to where we started - this weekend's concert. "I have no idea what my mother has in store," Goffin says, a twinkle in her eye. "Anything can happen!"

She will play her own set, and make a special appearance with her mother. And for those of you wondering what time to get to Hyde Park on Sunday, Goffin has an insider tip: "I come on at 3.40 so be there for 3.40. Tell everyone!"