David Cameron left his eight-year-old daughter in the pub following a Sunday lunch, after a mix-up with his wife Samantha, Downing Street has admitted.

The couple's daughter Nancy wandered off to the toilets while they were arranging lifts and they only realised she was not with them when they got home, the Sun said.

The prime minister rushed back to the Plough Inn in Cadsden, Buckinghamshire, where he found his daughter with staff.

A Downing Street spokesman said: "The prime minister and Samantha were distraught when they realised Nancy wasn't with them.

"Thankfully when they phoned the pub she was there safe and well. The prime minister went down straight away to get her." Downing Street said the incident happened "a couple of months ago".

The story could prove embarrassing for the prime minister, coming on the same day as the government relaunches its £450m troubled families programme.

The Camerons were at the Plough Inn, near Chequers, with Nancy and their other children, Arthur, six, and 22-month-old Florence, as well as two other families.

When Cameron left the pub he went home in one car with his bodyguards and thought Nancy was with his wife and their other children in another car. Samantha Cameron had assumed her eldest daughter was with her father. The mistake was only discovered when they got home.

The prime minister drove back to the pub and found Nancy helping staff. She was away from her parents for about 15 minutes.

A Downing Street spokeswoman said there was no question of the Camerons blaming security for the incident. "Sam thought the PM had Nancy, the PM thought Sam had Nancy," he said. "They take responsibility for their own children. No one is going to face disciplinary action."

The spokeswoman declined to discuss whether Cameron had drunk alcohol with his meal. "He had gone with friends at lunchtime, with a number of families with children, and they left in various different vehicles," she said.

"As you know, the prime minister is a very busy man but he always tries to live as normal a life as possible with his family."

The Sun quoted a Plough insider as telling the paper: "You'd have thought someone would have done a headcount or something.

"Pub staff found their daughter in the toilet and didn't know what to do.

"It's not like you can look up David Cameron in the phone book and then ring to say, 'You've left your daughter behind'.

"It's frightening the prime minister of Britain can forget something so important as his own daughter."