Downing Street said it had told members of Mr Trump's team that the allegations were “ridiculous” and should be “ignored”, after the claims were repeated by White House press secretary Sean Spicer.
Theresa May's official spokesman would not confirm whether the administration had offered an apology, but did indicate Mr Spicer had been told not to raise the claims again.
He confirmed that representations had been made by the British ambassador to the US and Ms May's national security advisor to members of Mr Trump's team.
The No 10 spokesman said: “We’ve made clear to the administration that these claims are ridiculous and they should be ignored and we’ve received assurances they won’t be repeated.”
He said that the situation would not damage the “special relationship”, and that it was close relations that the US and UK shared that allowed the Government to raise the matter.
Fox News commentator Andrew Napolitano alleged during a Fox & Friends broadcast earlier this week that Mr Obama had bypassed the US’s intelligence community and used the UK's spy centre to obtain details of Mr Trump's conversations, prompting a rare public and forthright response from GCHQ.
A spokesperson told CNN: “Recent allegations made by media commentator Judge Andrew Napolitano about GCHQ being asked to conduct ‘wire tapping’ against the then-President elect are nonsense.
“They are utterly ridiculous and should be ignored.”
The US Senate Intelligence Committee said earlier on Thursday there were “no indications” Trump Tower was under surveillance by the US government before or after the Presidential election.
President Donald Trump had used a series of Twitter posts to accuse his predecessor, Barack Obama, of wiretapping him.
In an interview on Wednesday with Fox News, Mr Trump suggested he first thought the former president was carrying out surveillance on Trump Tower after reading an article on the campaign in The New York Times.Reuse content