The two singers had been performing in Hyde Park on Saturday evening when their microphones were cut off.
Sir Paul had joined Springsteen on stage at the Hard Rock Calling music festival following a performance by the American rock star that had lasted more than three hours.
The US singer greeted Sir Paul saying “I’ve been waiting for this for 50 years”, according to members of the audience.
But after singing two Beatles hits both performers were forced to leave the stage in silence after their sound equipment was turned off - meaning they were unable to thank the audience.
The three-day event has a nightly noise curfew imposed at 10.30pm and Springsteen, who had been playing with his E Street Band, was due to play only from 7pm until 10.15pm.
Before Sir Paul joined him on stage Mr Springsteen performed hits such as Born In The USA and Because The Night.
He had earlier invited Rage Against The Machine’s Tom Morello on stage to perform two songs, and singer John Fogerty had joined him for one.
At one point he rewarded a fan’s loyalty by playing an obscure track that the man had requested by holding up a banner in the crowd.
The singer spotted the sign asking him to play the song Take ‘Em As They Come and said: “Tonight, my friend, this is your lucky night.”
He added: “It’s a completely obscure track I wrote for (the album) The River when I needed some rock songs.”
Audience members reacted angrily to the concert’s abrupt end.
Stephen Merchant, the comedian, wrote on the micro-blogging website Twitter: “Ashamed to be British right now. Springsteen and McCartney playing Twist & Shout in Hyde Park and council pulled the plug cos of curfew.”
Paul Simon will close the festival on Sunday night.
Last Updated: 07/15/12 15:43