Foreign Secretary Ed Miliband has thanked the US for its "tireless efforts" after Hamas announced it would disarm in exchange for the withdrawal of Israeli troops from Gaza.
Mr Miliband also praised Qatar, Turkey, and Egypt, welcoming the development.
US President Donald Trump stated on Thursday that the "agreement will be carried out in carefully structured phases".
In a statement, Mr Miliband said: “I welcome the announcement that Hamas will disarm.
“The focus must now be on implementing the 20-point plan in full. This includes the withdrawal of the IDF (Israel Defence Forces) from Gaza, and respect for the ceasefire by all parties.
“Conditions for the people of Gaza remain appalling. Israel must immediately end the unacceptable restrictions on aid, so that more food medicine and support can reach those who need it.
“The UK will keep working with all our partners as we seek to end the conflict in Gaza, and the terror threat from Hamas. We must reach a viable peace – with the Palestinian State and state of Israel living securely side-by-side.
“We thank the US, together with Qatar, Turkiye and Egypt, for their tireless efforts to progress these crucial negotiations.”
A peace deal put forward by the US last year would see Hamas relinquish its weapons, Israeli forces withdraw from Gaza as the disarmament progresses, and an international stabilisation force work with a new Palestinian police force until a new Palestinian government takes over in Gaza.
Egypt, which is mediating discussions between Israel and Hamas, said on Friday that both sides had agreed to a new 15-point roadmap and that a future meeting would be held in Cairo “to discuss implementation mechanisms”.
First Secretary of State Louise Haigh had earlier said that any progress in peace negotiations is “extremely welcome”.
She told BBC Breakfast: “We will need to await the Israeli government’s response and its commitment to the ceasefire and a way forward and a withdrawal from Gaza, and to cease its activities of settler violence and taking action against such settler violence in the West Bank.
“But if progress has been made, then it’s extremely welcome news, because the suffering in Gaza and the wider region has been too extreme for far too long, and the human cost of the war has been absolutely obscene and intolerable.”