Another four countries – the US, Australia, Italy and Canada – have also paused donations.
More than 1,200 people were killed when Hamas stormed Israeli communities.
The Foreign Office said in a statement the UK was “appalled” by allegations that UNRWA (United Nations Relief and Works Agency) staff were involved in the 7 October attack “a heinous act of terrorism” that the UK government has repeatedly condemned.
“The UK is temporarily pausing any future funding of UNRWA whilst we review these concerning allegations,” the statement said.
“We remain committed to getting humanitarian aid to the people in Gaza who desperately need it.”
The relief agency has played a key role in providing aid to the population of the besieged enclave amid a mounting humanitarian disaster.
Earlier this week the foreign secretary, Lord Cameron, called for more provisions to be allowed to enter Gaza during a visit to the region.
Sarah Champion, chair of the Commons International Development select committee, described the development as “very concerning”, saying that “in many ways, UNWRA effectively acts as the local authority, so the impact on civilians will be immense.”
But former immigration minister Robert Jenrick said he was “pleased” Britain had agreed to pause support for UNRWA, adding that “the UK has been too blasé about who we have funded and for what purpose. That needs to end now.”
The current crisis erupted on Friday when UNRWA chief Philippe Lazzarini said it had terminated contracts with “several” employees and ordered an investigation after Israel provided information alleging they played a role in the assault.
The US, the agency’s biggest donor, said allegations had been made against 12 employees.
UNRWA has around 13,000 staff in Gaza, almost all of them Palestinians. They range from teachers, in schools run by the agency, to doctors and other medical staff.
Israeli officials have frequently accused UNRWA of allowing anti-Israeli incitement. The Trump administration suspended funding to the agency in 2018, but it was restored by President Biden.
In its 7 October attack, Hamas broke through the security fence surrounding Gaza and stormed nearby Israeli communities, kidnapping some 250 people.
While some of the hostages have been released as part of transfer swaps with Israel, around 100 are still being held.