Former home secretary Alan Johnson has said there was a “glaring” mistake in the BBC hit series Bodyguard.

The politician revealed he has been enjoying watching the terror thriller, but said there were parts of the drama that just “wouldn’t happen”.

The series starred Keeley Hawes as the Home Secretary and Richard Madden as David Budd, the officer assigned to protect her, and showed the pair embarking on a passionate affair.

In November 2011, Johnson quit as shadow chancellor after his own police bodyguard was sacked by Scotland Yard following an investigation into an affair with the politician’s wife.

Appearing on ITV’s This Morning, where he was not asked about the affair, Johnson said he spotted a “glaring” scene that did not ring true in one of the episodes of the thriller.

Johnson, who served as home secretary from June 2009 to May 2010, said: “David Budd is in the restaurant with somebody else while the Home Secretary is having dinner and there are the two coppers plonked down at a table not eating or drinking anything.

“That wouldn’t happen because big signals are going off, ‘we are bodyguards’.

“What they do is blend in with the background and when you go for a meal they always come with you but they are there looking like two other diners so of course they have to order food.”

Johnson recalled learning of his promotion to the job while on a train returning to London from his constituency, and said: “When I pulled into King’s Cross I looked down and it was like a scene from a film, there were about five police officers with dogs, there were a lot of protection officers, there was a team of about 10 people waiting for me.”

Frank Armstrong, who served as head of protection for former prime minister Tony Blair, also pointed out errors in the programme that related to the PTSD suffered by Madden’s character.

He said: “To be a protection officer and certainly in such an important key position, there is a very high level of vetting.

“Your background is really looked into, all the checks are made and I don’t think he would have passed muster. He would have been out early on.”

Asked about the affair Budd had with the Home Secretary, Armstrong said: “If there is a series two there are a couple of issues that need resolving before he can resume his protection duties, one clearly is if that did happen, he would be off protection duties.

“Secondly, the illegal firearm he had in his possession, which I don’t think has been talked about that much, as if we always have stashed firearms in parts of our homes.

“Those were a couple of issues, but I thought it was great entertainment and loads of people are asking me, is it really like this, and I said it’s not as exciting as David Budd.”

Creator Jed Mercurio has vigorously defended the research he did while writing the show, responding to one critic on Twitter: “I did listen to the police advisors. There were three of them. One was a former PPO. One was a former DCC. One was a serving Inspector. I’ll take their advice over yours.”