Sir Peter Westmacott, who was the UK's top diplomat in the U.S. until January, also urged the White House to pubicly accept British assurances that the allegation about GCHQ is nonsense.
"This is a risky game", Westmacott warned in an opinion piece in The Guardian.
On March 4, the NY billionaire attacked Obama in a tweet, claiming that he had "tapped" his phone while he was busy campaigning for the November 8 vote, further suggesting that the British intelligence was also involved in the move. "It is critical to our shared efforts to counter terrorism".
America and Britain's relationship has been unexpectedly strained this week over unsubstantiated allegations that British spy agency GCHQ helped Obama tap Donald Trump's phones at Trump Tower.
He added that "gratuitously damaging" the nations' alliance with lies without setting the "record straight would be a gift to our enemies they could only dream of". "Second, the idea of the British foreign secretary signing a warrant authorizing such an intrusion into domestic U.S. politics was unthinkable".
Westmacott also referred to Trump's "famous reluctance to admit mistakes".
His intervention came after White House press secretary Sean Spicer during one of his daily press briefings last week cited a claim by a Fox News analyst that Mr Obama had used GCHQ to bug Trump Tower.
It led to U.S. officials making an apology for repeating the claims which had been initially made on Fox News.
GCHQ responded by saying the allegations were "nonsense, utterly ridiculous and should be ignored".
When Trump was questioned about the "wiretapping" saga during a meeting with German chancellor Angela Merkel on Friday, Trump said Spicer was simply repeating a media report, the Huffington Post reports. I didn't make an opinion on it. You shouldn't be talking to me.
Earlier on Sunday, California Republican Representative Devin Nunes, the chairman of the House Intelligence Committee, also pushed back against the claims, asserting that "there was no FISA (Foreign Intelligence Surveillance Act) warrant" for wiretapping.
Trump also hinted at the unsubstantiated allegation during a press conference with Germany's Angela Merkel, suggesting both of them had been surveiled by U.S. intelligence services - a reference to reports that USA spy agency the NSA had tapped Merkel's phone.