Britain has joined 13 other Security Council members and backed a United Nations resolution that rejected the recognition of Jerusalem as Israel’s capital. The resolution was vetoed by the United States.
The vote offered a display of international condemnation following Donald Trump’s announcement on December 6 that the US would move its embassy to the holy city.
Trump sparked protests across the region after upending decades of US policy towards the Middle East by announcing he recognised Jerusalem as Israel's capital earlier this month.
May said at the time she regarded the decision as "unhelpful for prospects for peace in the region."
Speaking after Monday's vote in New York, Britain's UN ambassador Matthew Rycroft said: "The status of Jerusalem should be determined through a negotiated settlement between the Israelis and the Palestinians, and should ultimately be the shared capital of the Israeli and Palestinian states."
The vetoed resolution would have demanded that all countries comply with earlier Security Council decisions on Jerusalem, dating back to 1967, requiring the city's final status to be decided in direct negotiations between Israel and the Palestinians.
Any decisions by a UN member state which purport to alter the status of the city "have no legal effect, are null and void and must be rescinded", said the resolution, tabled by Egypt.
There was never any question of the US opting not to exercise its veto on a resolution which would have had the effect of forcing Trump to reverse his decision.
US ambassador Nikki Haley called it "an insult" and said she wielded the veto "in defence of American sovereignty and in defence of America's role in the Middle East peace process".
Palestinians immediately said they would seek a similar resolution in the 193-member UN General Assembly, where there are no vetoes but decisions are not legally binding.