The band, fronted by Thom Yorke, have been asked to reconsider performing there as part of an ongoing cultural boycott.
Other signees include South African archbishop Desmond Tutu, Wolf Hall director Peter Kosminsky, Juliet Stevenson, Ricky Tomlinson, Miriam Margolyes, Alexei Sayle and Roger Waters.
The letter was organised by Artists for Palestine UK and asks Radiohead not to perform in a country where ‘a system of apartheid has been imposed on the Palestinian people’.
‘In asking you not to perform in Israel, Palestinians have appealed to you to take one small step to help pressure Israel to end its violation of basic rights and international law,’ it reads.
Radiohead are accused in the letter of double standards as the band supports Tibet’s fight for independence.
‘Since Radiohead campaigns for freedom for the Tibetans, we’re wondering why you’d turn down a request to stand up for another people under foreign occupation.’
It adds: ‘Surely if making a stand against the politics of division, of discrimination and of hate means anything at all, it means standing against it everywhere – and that has to include what happens to Palestinians every day.’
Director Loach said the band should cancel the gig ‘for their own self respect’ in a separate comment.
The band are due to play Park Hayarkon in Tel Aviv on July 19.
A spokesperson for Radiohead said the group has no comment.
The Guardian points out that guitarist Jonny Greenwood is married to Israeli artist Sharona Katan, while he recently released an album with the Israeli singer Shye Ben Tzur.