Prime minister Boris Johnson’s official spokesman refused to comment on Trump’s decision.
The UK is one of the biggest donors to the WHO, with an annual fee of around £17m and much larger sums in voluntary contributions to its projects. Already, Britain has given £75m to help it respond to the spread of coronavirus.
But the multilateral body has come under fire for failing to hold China to account for withholding vital information about Covid-19 in the months after it first emerged in the city of Wuhan at the end of last year.
Mr Johnson's spokesman said that Britain wanted the WHO to "learn lessons" from its handling of the crisis.
“Our position is that the UK has no plans to stop funding the WHO, which has an important role to play in leading the global health response," said the PM's spokesman.
“Coronavirus is a global challenge and it’s essential that countries work together to tackle this shared threat.”
Asked if the Government was disappointed by Donald Trump’s move, the spokesman said: “I can only set out the UK’s position and that is we have no plans to stop funding the WHO.”
The spokesman played down suggestions that the UK could step in to make up the loss to the WHO of Trump's move, saying that contributions were based on the UK's assessment of the organisation's needs and were "not something that is affected by other countries' decisions on funding".
Mr Trump justified the suspension of US payments by saying the WHO had "failed in its basic duty" to obtain, vet and share information in a timely fashion and accused it of spreading Chinese "propaganda”.
While stopping short of any direct criticism of the organisation, Mr Johnson's spokesman used diplomatic language to indicate that London believes it can up its game.
"We want to see the WHO continue to learn lessons on how to improve its response to global health emergencies," he said.
And he was equally diplomatic over allegations that China failed to share information on the deadly virus as quickly and openly as it should.
"We have always stressed that transparent and accurate information about the virus is essential for an effective global response," said the PM's spokesman.
"And we have also been clear that we want to work with all parts of the international community, including China, to ensure a joined-up response to the epidemic."
Former prime minister Gordon Brown described Trump's move as "an act of self-harm on the part of America".
Mr Brown told the BBC's HardTalk that the US president had signed up to a G20 commitment to support the WHO as recently as 26 March and should be held to it by other world leaders.
"It’s our duty to persuade the Americans solidarity is in their self-interest," said the ex-PM.
The former head of the secret intelligence service MI6, John Sawers, said it would be better to hold China responsible rather than the WHO.
“There is deep anger in America at what they see as having been inflicted on us all by China and China is evading a good deal of responsibility for the origin of the virus, for failing to deal with it initially,” Sawers told the BBC.
“Intelligence is about acquiring information which has been concealed from you by other states and other actors, there was a brief period in December and January when the Chinese were indeed concealing this from the West.”
And former chancellor Sajid Javid said Trump was wrong to cut funding to the WHO at a time of global health emergency.
Mr Javid told BBC Radio 4’s Today programme: “Whilst there are legitimate questions to ask about the WHO, I think that now it’s not the time and that’s the wrong thing to do.”
He added: “I think one of the lessons to learn from this when we are past the worst of the crisis is that we are going to have to look carefully into was China providing the right information… to the WHO and to the others.
“China didn’t even admit to human-to-human transmission until some time in January, which was very late in the day and I think it’s a legitimate question to ask what they knew, when and how that could have made a difference.”
Liberal Democrat foreign affairs spokesperson Alistair Carmichael said: "Trump's decision to halt funding for the World Health Organisation at this moment is a dereliction of duty and puts lives at risk around the world.
"The UK has a duty to lead and the foreign secretary must do everything in his power to bring the US president back on board in supporting the efforts of the World Health Organisation. The government must do everything possible to ensure this vital institution is not undermined at the moment we need it most."
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