UK Prime Minister Gordon Brown is due to hold talks with Israeli counterpart Benjamin Netanyahu on the future of the Middle East peace process.
During a Downing Street meeting, Mr Brown is likely to push for a halt to Israeli settlement building.
Mr Netanyahu is also due to meet German Chancellor Angela Merkel and US Middle East peace envoy George Mitchell.
The Israeli leader is taking part in a four-day tour of Europe, having arrived in the UK on Monday.
Mr Brown has repeatedly called for a freeze on settlements, warning that the issue is an obstacle to peace in the Middle East.
He told Ehud Olmert, Mr Netanhayu's predecessor, last year in Downing Street that the settlements issue was a "barrier" to peace which must be overcome.
Israel has also been under strong pressure from the US administration on this issue.
At his first press conference since returning from holiday, Mr Brown is also likely to be asked for his reaction to the release of the only man convicted of the Lockerbie bombing.
Mr Brown has been criticized for not commenting on the Scottish government's decision to free Abdelbaset Ali Mohmed Al Megrahi on compassionate grounds, allowing him to return to Libya.
Opposition parties have accused him of a "deafening silence" on the issue but No 10 has insisted it is a matter for the devolved administration in Edinburgh.
The Israeli prime minister will meet President Barack Obama's envoy George Mitchell in London on Wednesday.
Mr Obama is working on a Middle East peace plan which is due to be unveiled this autumn.
Palestinian Prime Minister Salam Fayyad told the BBC he wanted those meeting Mr Netanyahu this week to leave him in no doubt that Israel has to stop building homes on occupied land.
Mr Netanyahu can expect criticism of Israel's West Bank settlements from Gordon Brown. But this will be criticism delivered sotto voce. British officials don't want to upset negotiations, which are at a very delicate stage. And while Britain sees the settlements on occupied land as a breach of international law, it still counts itself - in Mr Brown's words - a "true friend" of Israel.
The US has been calling for a freeze in settlement building. Mr Netanyahu's important meeting in London, therefore, will be on Wednesday, with the US special envoy George Mitchell.
There will be other things to talk about at the Downing Street meeting. Mr Netanyahu will be looking for British help in keeping the pressure on Iran over its nuclear programme. He has often said that he sees no greater threat to Israel - and the peace of the wider world - than a nuclear-armed Iran. Britain, too, has been in the lead in taking international action over Iran. How, though, will Mr Brown respond if the Israeli prime minister demands a 'Plan B', should economic and diplomatic sanctions against Iran fail?
"Unless we do this decisively and convincingly, how are we to expect people on both sides of this divide to buy into this process?" he said.
The BBC's Middle East editor Jeremy Bowen said reports in Israel suggested some sort of settlement freeze could be close, perhaps in return for concessions from Arab states.
"But before he left Israel, Mr Netanyahu said he would not allow anything to compromise Israeli sovereignty in Jerusalem, part of which is also claimed by the Palestinians as a capital," he said.
He added the Israeli PM would be pressing Downing Street for the toughest measures necessary to stop Iran getting nuclear weapons.
Mr Netanyahu said on Sunday that stalled peace talks between his government and the Palestinian Authority could resume in September.
The Israeli government is currently not issuing tenders for housing on settlements in the occupied West Bank. Officials have said this does not amount to a settlement freeze.
Israeli groups that monitor settlement building say that settlement activity may have actually increased in recent months.
On the ground, construction continues at government-fundedprojects, by private sector companies and at unauthorized outposts, the groups say.
About 500,000 Jews live in the West Bank and East Jerusalem settlements, which are illegal under international law, among 2.5 million Palestinians.
The land was captured by Israel in the 1967 war and Israel insists its undecided status means the settlements are legal. But Palestinians view them as constituting the theft of their homeland, while new settlement building further jeopardizes their prospects of establishing an independent state.