Sky News has published part of Westminster Accounts, a joint project between them and Tortoise Media to shine a light on how money works in UK politics.
I decided to have some fun with this after being informed about it by my friend JJ.
So I searched by funding source, entering the search string ‘palestinian,’ which yielded two results:

The ICJP funding all went to one MP: Crispin Blunt:

Blunt has been described as a “long-term critic of Israel,” but I would call him a hater. He once faced calls to be removed as the whip after he suggested that terrorist group Hamas had a right to hit “legitimate targets” in Israel during a parliamentary debate.
His receiving over the average UK salary‘s worth of gifts from the anti-Israel ICJP might put his views into perspective.
As for Medical Aid for Palestinians, the second palestinian group I found dispensing gifts to MPs, there were no huge amounts:

On the flipside, I decided to also enter the search string ‘Israel’, which yielded these results:

The only substantial amount came from Conservative Friends of Israel, but a drill-down shows the gifts were spread among 40 MPs, with the top amount being £5,920:

Entering ‘Jew’ in the search string yields similar results – no large gifts of note:

In other words, while the haters love to allege there is some powerful Israel lobby operating in the UK – a lobby that was allegedly responsible for an “antisemitism witch-hunt” against Jeremy Corbyn – the Westminster Accounts do not support this allegation. If anything, it is an anti-Israel group that might be exerting some influence over an anti-Israel MP.
Update: Compare and contrast:


Update: It was reported in August 2022 that Blunt was under investigation by the parliamentary watchdog after failing to declare these payments.