There are few places in London where the city’s past, present and future meet so seamlessly as they do in Princelet Street. Here, in the heart of Spitalfields, a row of Georgian townhouses — once grand family residences, later a place of shelter for newly arrived immigrants, now showing more than a hint of gentrification — stand in the shadow of the glistening glass towers of the City of London.

It is appropriate, therefore, that 19 Princelet Street should house the Museum of Immigration and Diversity; a monument to, and reminder of, the waves of migrants who have been swept on to Britain’s shores and who have gone on to ceaselessly shape and reshape the face of its capital city.

Beyond its double doors — a reminder that this building has been changed by multiple uses, and many people — is the entrance hall to a family home. One of a matching pair, No19 was built in 1719 by Samuel Worrall, a carpenter.

Early tenants included a Huguenot refugee family: Peter Ogier, a master silk weaver, his wife and eight children. Around 50,000 Protestants fled to London to escape persecution in Catholic France; the Ogiers were just one of at least eight Huguenot households on this side of Princelet Street.

But the dour green Second World War utility paint which adorns the walls of the entrance hall belies the jewel beyond them. Much of the back wall of the house has been removed, allowing one to step into a synagogue which was built in 1869 by Russian and Polish Jews to whom the building had been leased.

Etched in gold leaf along the balcony panels are the names of the benefactors. Alongside a roll-call of the upper echelons of Anglo-Jewry — Mocatta, Rothschild, Montague — are the names of more anonymous families giving small amounts, marking marriages and deaths. Above the balconies hang huge chandeliers adorned with double-headed eagles. From the Victorian glass roof, pink-and-green speckled daylight fell on to the bimah. It now awaits repair in a front room. Upstairs, the museum lovingly stores other treasures, including a sequin-studded Torah mantle and a board on which gifts — three velvet cushions, a suit, a pair of silver bells — were recorded.

The members of this new synagogue were recent arrivals with big ambitions; the synagogue was modelled on the Grand Synagogue in Liverpool. This was not only a busy place of worship — in the 1880s, there were up to nine weddings a day — it was also a hub of activism. In the basement, anti-fascist activists plotted tactics before the Battle of Cable Street.

The second oldest in London, the synagogue closed in the 1960s, although it continued to be in occasional use into the 1970s. By then, of course, new generations of migrants had largely replaced the Jews.

The beauty of this place stems from the manner in which those who have lived, worked and worshipped here seem somehow to overlap. The parlour where the Ogier children studied was, a century later, a religious school for Jewish boys. A further century on, Bangladeshi women learned English here.

The museum’s centrepiece — an installation entitled Suitcases and Sanctuary — was created by schoolchildren from six local schools, enabling them to explore the experience of successive groups of migrants. A group of Bengali Muslim children tell the Jewish story. On a video, they relate a Yiddish folk story about a shopkeeper dealing with antisemitism; in a suitcase, they have written luggage labels describing why Russian Jews were forced to leave the Pale of Settlement.

The exhibit’s power rests on its empathy and simplicity; its ability to convey the world through the eyes of children. In other rooms, children showcase the lives of Irish, Caribbean, Bengali and Somali migrants.

While the museum opens its door to many groups throughout the year, it is hobbled by a lack of funds. Much rests on a National Lottery bid under consideration this summer. It would enable more regular openings and the rest of the building to become part of the museum. It includes a weaver’s attic workplace that was once home to David Rodinsky, an unpaid synagogue caretaker who spoke 15 languages and was said to be compiling a universal dictionary.

Rodinsky vanished one day in 1969. His room lay untouched for a decade; 20 years later, his story was told by Iain Sinclair and Rachel Lichtenstein in their book, Rodinsky’s Room (Granta Books).

“Every schoolchild in England should see this,” wrote the late Bernard Crick of 19 Princelet Street. So should every adult. If ever there was a moment when Britain needed to be reminded of the immigrant lifeblood which has coursed through its veins for centuries, it is now.

19 Princelet Street has two free summer openings this month. On Sunday June 18, 2pm to 6pm as part of the Jo Cox Great Get Together and Sunday June 25, 2pm to 6pm as part of Refugee Week