Barack Obama will seek a joint Middle East agreement with David Cameron, insisting that a Palestinian state should be based on pre-1967 borders – a proposal rejected by Israel's prime minister as "unrealistic" and "indefensible".

The issue will be raised in private talks between the two men during the state visit by Obama and his wife to London, only the third by a US president in 100 years. Afghanistan, Libya, relations with Pakistan and the global economy – as well as the vacancy for the top job at the IMF – will also make up the agenda.

Despite the outright rejection by the Israeli premier, Binyamin Netanyahu, of a Palestinian state based on the borders that existed before the Six Day War, when Israel captured and occupied the West Bank and Gaza, Obama has already secured the political backing of the United Nations, European Union and Russia who, with America, are collectively known as the "quartet".

Signalling his determination to keep up pressure on Israel, Obama will be looking to enlist the public support of the UK prime minister. The aim is, in large part, to persuade the Palestinian leadership not to go to the UN in September seeking symbolic backing for an independent state.

The coming meeting between the two men follows evidence of a hardening of criticism of Israel by London. On the eve of the Obamas' arrival, Middle East minister Alistair Burt accused Israel of "unhelpful and destabilising activity" in announcing the building of 1,500 new settlement units in East Jerusalem ahead of a speech by the president on the Middle East on Friday.

"I am deeply disappointed with Israel's announcement on 19 May to build up to 1,500 settlement units in the East Jerusalem settlements of Har Homa and Pisgat Ze'ev," Burt said.

"This decision came on the same day as Obama's important speech on the Middle East, which set out a clear path towards peace between the Palestinians and Israelis. Settlement activity is a recognised obstacle to this path. It is illegal under international law and should stop.

"The UK continues to call on Israel to cease unhelpful and destabilising activity and instead help build the conditions that allow meaningful negotiations to resume."

UK sources said they expected a packed agenda, with the two leaders likely to set aside time to discuss the enhanced threat of global terrorism following the death of Osama bin Laden, progress in Afghanistan and the west's strategy to oust Muammar Gaddafi from power in Libya.

Away from the formal agenda of talks, the president's wife, Michelle, and the prime minister's wife, Samantha, will host a barbecue in the Downing Street garden on Wednesday evening for British and US troops who have served in Afghanistan and Iraq, including some who have suffered injuries.

The president and prime minister will attend and lend a hand dishing up the food. "They will be helping with the serving. There will be British sausages and burgers on the menu," said a spokeswoman.

The president and his wife, who will begin their tour of Europe in Ireland on Monday, will stay at Buckingham Palace for the UK leg of the visit, which begins on Tuesday and ends on Thursday.

They will be met by the Prince of Wales and Duchess of Cornwall before flying to the palace. On Tuesday evening there will be a state dinner at the palace preceded by meetings with Cameron and Labour leader Ed Miliband.

Cameron and Obama will hold further talks on Wednesday, when the president will also address both houses of parliament in Westminster Hall. He will lay a wreath at the Grave of the Unknown Soldier in Westminster Abbey.

Liberal Democrat sources expressed frustration yesterday at reports that Nick Clegg had been "snubbed" by the president. The Lib Dems say it was made clear that US protocol did not allow for the president to have a bilateral meeting with the Liberal leader in his role as deputy prime minister.