All but one were released after being treated for the effects of smoke inhalation. One woman was kept in overnight for observation.
The fire broke out at Earls Court station shortly after lunch. It was linked to a power failure at the Lots Road power station in Fulham, west London.
The Underground network was crowded with Easter weekend shoppers, tourists and people travelling to football matches and the Oxford/Cambridge Boat Race. Several soccer kick-offs were delayed to allow fans to arrive.
Services on the network were reduced by 90 per cent, trapping people in carriages in tunnels and at stations. An Underground spokesman said it was the "biggest problem ever".
This is not the first time the gas-fuelled Lots Road power station has caused problems. Two years ago to the day, on 6 April 1994, 100,000 passengers were trapped in 300 trains for up to 75 minutes when someone turned off the plant's gas supply by mistake.
Brian Wilson, Labour's transport spokesman, said yesterday the failure of the system was a "classic example" of the Government's wider failure to invest in public transport.
In the past month, ministers have brought forward plans to privatise the troubled Lots Road power station.
"It's the only thing they can think of doing," said Mr Wilson. "Instead of investing in the capital's transport system they become obsessed with the desire to privatise."
By mid-afternoon, power had largely been restored to the Tube system. Only the east-west District Line remained paralysed. Meanwhile a telephone system failure left Underground staff with only two lines on which to give out information.