UK Prime Minister Gordon Brown has said he is "more optimistic" about Middle East peace after talks with with Israeli counterpart Benjamin Netanyahu.
After the Downing Street meeting, he stressed that Britain was a "true friend" of Israel.
But he stressed that it was necessary to remain "realistic" in efforts to secure lasting peace.
Mr Netanyahu said a demilitarised Palestinian state was needed if this is to be attained.
Mr Brown has repeatedly called for a freeze on Israeli settlement building, warning that the issue is an obstacle to peace in the Middle East.
US pressure
During the Downing Street press conference, he said he "deplored" recent comments about the Israeli regime made by the Iranian government.
The UK and Israel shared the same concerns over the possibility of Iranian nuclear weapons, he added.
Mr Netanyahu is also due to meet German Chancellor Angela Merkel and US Middle East peace envoy George Mitchell during his four-day tour of Europe.
Israel has also been under strong pressure from the US administration on this issue of settlements.
President Barack 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.
"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-funded projects, by private sector companies and at unauthorised 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 jeopardises their prospects of establishing an independent state.
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