Thornberry, who served in Labour’s shadow cabinet for more than a decade, also accused Knesset members of being “remarkably rude” to the UK delegation.
The Labour MP called on the British government to respond, denouncing Haskel’s actions as “unacceptable.”
But a senior source who was at the meeting said: “It was obvious to everyone in the large committee room that the meeting was being filmed. No one from the British delegation asked for Chatham House rules or said the meeting was off record.”
Thornberry also pressed Middle East Minister Hamish Falconer on how he intended to respond to her allegations. Falconer said he would investigate the matter and “come back to the committee.”
She asked Falconer, “Would you expect, minister, if there was a visiting delegation of Members of Parliament to the House of Commons, for the delegation to be videoed without their knowledge of consent? Or for it to be put onto Instagram and indeed briefed to the Daily Telegraph in disparaging terms?”
Falconer told Thornberry that he was not "familiar with the details" but that if "someone was visiting the House of Commons, we want to show them courtesy".
Continuing her attack on the Knesset, Thornberry added that it would be “particularly bad, wouldn’t it, if it was the deputy foreign minister of Israel, who would be videoed in the UK and for disparaging comments to be made about her evidence or private meeting which she had let’s say with us.”
“Because the opposite has just happened with us, and a video of us at the Knesset meeting with the Deputy Foreign Minister has been posted on Instagram.
"Certainly, we had no knowledge that it was being videoed and assumed of course that it would never happen. I have just found out about it is, and to say that I’m cross might be an understatement,” Thornberry went on.
The MP for Islington South and Finsbury accused members of the Knesset of being “quite provocative” and “quite insulting,” with a “remarkably rude” attitude. She claimed that the UK delegation did "their utmost to keep their decorum and remain polite".
During the 60-second clip of the meeting, which was visible on the Israeli minister's Instagram page on Tuesday and later removed, Haskel asked Thornberry if she had spoken to Palestinians from the occupied West Bank about how they would vote if elections were to occur.
“What happens if there are elections tomorrow in the West Bank? Did you go there to talk to them? Why haven’t there been elections there?”
During her response, Haskel interrupted Thornberry, saying: "The fact is that there are no elections because the day after Hamas is going to take control."
The Israeli minister went on, “If we agree in any way to a two-state solution... Gaza is going to be in the hands of Hamas again. So, you’re asking me to give Gaza again to Hamas.
“When people come and tell us, ‘You need to do the two-state solution now,’ for us it means in reality you give it to Hamas,” she said in the video – which focused on the minister’s comments about a two-state solution, rather than Thornberry’s reply.