Image caption North Korea's team returned to the field about an hour after the mistake was pointed out

Olympic organisers have apologised to North Korean athletes whose images were shown next to the South Korean flag.

The mix-up delayed the women's football match, at Glasgow's Hampden Park on the first day of sporting action.

The men's football gets under way later, with matches including Britain v Senegal at 20:00 BST (19:00 GMT).

Speaking to BBC News, Prime Minister David Cameron highlighted benefits of the Games, and said: "The real legacy is the inspiration to young people."

He added: "People are going to be coming to our country over the next few weeks and seeing a really inspiring sight.

"That's about a people's Olympics, not a government Olympics."

In other news:

'Very upset'

Media playback is unsupported on your device Media caption Flag error offends North Koreans

The BBC's sports editor David Bond said the flag mix-up at Hampden Park had been an "embarrassing mistake" and not the start Games organisers would have wanted, but "no great harm was done".

As the North Korean players were being introduced before the match against Colombia, South Korean flags were mistakenly displayed in the video package.

The squad walked off and could only be persuaded to return when the teams were announced again with each player's face displayed next to the North Korean flag, delaying kick-off by about an hour.

Relations between the two Koreas are tense - they remain technically at war following the 1950-53 Korean conflict, which ended in an armistice.

Speaking after the match, North Korea's coach Sin Ui Gun said: "Our team was not going to participate unless the problem was solved properly...

Image caption The error saw North Korea's flag (top) replaced by the South Korean flag (bottom)

"Unfortunately it took some time later for the broadcast to be done again properly and we made the decision to go on with the match."

It was not immediately clear who had produced the video shown in the stadium.

London 2012 spokesman Andy Mitchell said: "The South Korean flag was shown in the video package on the screen before the kick-off and the North Koreans were naturally very upset about that...

"A genuine mistake was made for which we apologise."

BBC Scotland football reporter Alasdair Lamont said that during the delay to the game the crowd had become frustrated at a lack of information.

"I don't think there was any reason given the entire time before the kick-off eventually took place as to why there had been a hold-up," he said.

"They were simply given a couple of messages saying there was 'an issue behind the scenes, we're doing our best to resolve it', and that was basically it."

One spectator, Paul, told BBC Radio 5 live: "An announcement was made that there was a technical problem behind the scenes, and even then when the players came back on, they came back on for a second warm-up, and quite a large portion of the crowd started booing."

Media playback is unsupported on your device Media caption Paul Deighton: It was a simple human error, that's why we've apologised

North Korea's state news agency KCNA made no mention of the blunder in its report on Thursday of the team's 2-0 victory over Colombia.

North Korea will face South Korea in the first round of the men's Olympic table tennis team event after the pair were drawn against each other on Wednesday.

'Value for money'

In an interview on BBC Breakfast, asked about benefits to the wider UK from the London 2012 Games, Mr Cameron said: "I think we will get value for money as a country."

He said that the Games were expected to come in under their £9bn budget, while there were predicted to be "£13bn in economic benefits from the deals that are going to be done, the extra spending, the extra tourism and all the rest of it".

The nation would enjoy the physical infrastructure left by the Games, he said, giving the example of the aquatics centre's expected 800,000 visitors a year.

"But the real legacy is the inspiration to young people who will want to take up sport, who will be inspired by the competitive ethos of the Olympics, who will see Britain at its best," the prime minister said.

The opening match in the men's football gets under way at 12:00 BST at Hampden Park when Honduras take on Morocco, followed by Spain v Japan.

Matches are also taking place at St James' Park in Newcastle, Cardiff's Millennium Stadium and the City of Coventry Stadium.