Israeli Prime Minister Benjamin Netanyahu met with his British counterpart Gordon Brown on Tuesday afternoon at the Downing street No. 10.
Netanyahu arrived in London on Monday and is expected to hold talks with the U.S. Middle East envoy George Mitchell in London on Wednesday. The four-day European tour will also take him to Berlin, where he will meet Chancellor Angela Merkel on Thursday.
During a joint news conference after the meeting, Brown said he is more optimistic about Middle East peace after talks with the Israeli prime minister.
"We've had good talks", which "leaves me as realistic as ever, but more optimistic than before," Brown said.
The two leaders discussed the issue of Israeli settlements, which Brown considered as a barrier to peace in the Middle East.
But he said "I am increasingly confident. that there is a genuine will to make progress that a freeze of such activity would result in meaningful steps towards normalization from Arab states."
Netanyahu said a demilitarised Palestinian State was needed if this is to be attained, adding that "We're working hard to advance a peace process that will lead to an actual peace result. And we hope to move forward in the weeks and months ahead."
Israel has removed 147 checkpoints in the West Bank, the Israeli Prime Minister said, "We have moved, we expect similar movement from the Palestinian Authority".
"We expect Palestinian partners to be courageous partners for peace," he added.
In addition, Britain and Israel shared the same concerns over Iranian nuclear issue.
Brown said: "If there is no further progress immediately then I believe the world will have to look at stepping up sanctions against Iran as a matter of priority."
Some people, who support a two-state solution of their conflict, held a demonstration at the Downing Street, shouting that "We are Palestinians" and "Free Palestine".
The bilateral meeting was overshadowed by the Lockerbie row as Brown was asked about his comments on the release of Lockerbie bomber at a press conference in the Downing Street after talks with Netanyahu, his first official engagement since returning from holiday.
Brown said he was "angry and repulsed" by Libyan welcome for Abdelbaset Ali al-Megrahi and insisted that the resolve to fight terror is absolute.