* Britain criticises Kerry over Israel comments
* Says not right to criticise composition of Israeli government
* PM May edges closer to President-elect Donald Trump
* United States says surprised by British remarks
* Western divisions over Obama's Israel policy emerge (Recasts, adds details)
By Guy Faulconbridge and Kate Holton
LONDON, Dec 30 (Reuters) - Britain scolded U.S. Secretary of State John Kerry for describing the Israeli government as the most right-wing in Israeli history, a move that aligns Prime Minister Theresa May more closely with President-elect Donald Trump.
After U.S. President Barack Obama enraged Israeli Prime Minister Benjamin Netanyahu by refusing to veto a UN Security Council resolution demanding an end to Israeli settlement building, Kerry's public rebuke of Israel has unsettled some allies such as Britain.
Amid one of the United States' sharpest confrontations with Israel since the 1956 Suez crisis, Kerry said in a speech that Israel jeopardizeds hopes of peace in the Middle East by building settlements in the occupied West Bank and East Jerusalem.
While Britain voted for the UN resolution that so angered Netanyahu and says that settlements in the occupied territories are illegal, a spokesman for May said that it was clear that the settlements were far from the only problem in the conflict.
In an unusually sharp public rebuke of Obama's top diplomat, May's spokesman said that Israel had coped for too long with the threat of terrorism and that focusing only on the settlements was not the best way to achieve peace between Jew and Arab.
London also took particular issue with Kerry's description of Netanyahu's coalition as "the most right-wing in Israeli history, with an agenda driven by its most extreme elements."
"We do not believe that it is appropriate to attack the composition of the democratically-elected government of an ally," May's spokesman said when asked about Kerry 70-minute speech in the State Department's auditorium.
The U.S. State Department said it was surprised by the remarks from May's office and said Kerry's comments were in line with Britain's own policy. It pointedly also thanked Germany, France, Canada, Jordan, Egypt, Turkey, Saudi Arabia, Qatar, the United Arab Emirates for support.
TRUMP AND MAY?
Britain has long cherished its so-called "special relationship" with the United States as a central pillar of its foreign policy, but May has struggled to build relations with Trump's transition team.
Following his election, Trump spoke to nine other world leaders before he spoke to May while he caused astonishment in London when he suggested that Brexit campaigner Nigel Farage should be Britain's ambassador to Washington.