The US has agreed not to repeat claims the UK's communications intelligence agency wiretapped Donald Trump during the presidential election campaign.
GCHQ rejected allegations made by White House press secretary Sean Spicer, that it spied on Mr Trump, as "nonsense".
No 10 has now been assured by Mr Spicer he would not repeat the accusation.
A spokesman for Prime Minister Theresa May said it had been made clear to US authorities the claims were "ridiculous and should have been ignored".
GCHQ also rejected the allegations as "utterly ridiculous". The unusual move by the agency to comment on the news came after Mr Spicer cited claims first made on US TV channel Fox News earlier this week.
Mr Trump said that Trump Tower in New York was under surveillance, but has provided no evidence for the claim.
The allegations of GCHQ involvement were initially made by former judge Andrew Napolitano.
Mr Spicer quoted Mr Napolitano as saying: "Three intelligence sources have informed Fox News that President Obama went outside the chain of command."
He said Mr Obama "didn't use the NSA, he didn't use the CIA, he didn't use the FBI and he didn't use the Department of Justice, he used GCHQ.
"What the heck is GCHQ? That's the initials for the British spying agency. They have 24/7 access to the NSA database."
A GCHQ spokesman said: "Recent allegations made by media commentator Judge Andrew Napolitano about GCHQ being asked to conduct 'wiretapping' against the then president-elect are nonsense.
"They are utterly ridiculous and should be ignored."