Intensive ferry shuttle services will run through the night from Dover to Dunkirk, Boulogne and Calais to help clear the backlog of traffic in Kent.
Elsewhere freezing conditions caused travel disruption in the south and east of England and blizzards caused dozens of accidents across Scotland.
Flights in and out of London suffered delays, with 26 cancellations throughout the day at Heathrow Airport, a BAA spokesperson said.
Breakdown recovery service the AA said call-outs were up 250% on a normal Saturday to around 20,000, and more snow is expected in Wales, Northern Ireland and northern England.
During the Eurostar delays some passengers were stuck on a train for up to seven hours in sidings in Folkestone.
Lucy Morris' 2hr 20min journey from Paris took her more than 16 hours.
She was stuck in the Channel Tunnel for about five hours and after her train was towed out, she was transferred on to another train, which was stuck in the sidings.
The 20-year-old student from London, who had been on a shopping trip, said: "There has been no proper organisation.
"There is water but people are hungry. Staff are pleasant but have no idea. I'm exhausted and also angry at being treated so badly."
How passengers were rescued
The company plans to offer passengers a full refund for tickets , another free journey with them and £150 compensation.
Responding to criticism over the handling of the situation, Eurostar's chief executive, Richard Brown, said: "We did get them all safely out of the tunnel. Safety is our absolute priority as you would expect.
"What was unprecedented was the weather conditions particularly in northern France with heavy snowfall and very, very cold temperatures outside of the tunnel."
Mr Brown said the conditions caused condensation which brought about electrical problems in the tunnel.
He added: "It is utterly unprecedented to have five trains failing in the tunnel at the same time. We will obviously be looking very closely at this to make sure that is does not happen again."
Transport Minister Chris Mole backed plans for an investigation into the causes of the delays.
He said it was clear that passengers had a distressing experience.
Passengers on two of the trains were taken out via service tunnels to car trains, while the passengers on the other three trains remained on board.
Eurostar chief says 'sorry'
Eurostar said there would be a limited service on Sunday and asked passengers whose journeys were not essential to consider cancelling their trips. It hopes to have a full service by Monday.
The problems with the Eurostar services had a knock-on effect for car passengers hoping to use the tunnel.
James Brownell and his friends had a 12-hour wait at Folkestone.
The 27-year-old from Essex said they were left in their car in "sub zero temperatures" but they luckily had duvets and blankets to keep them warm.
John Keefe from Eurotunnel, the operator of the Channel Tunnel, said motorists should not travel unless they have a confirmed booking.
He said those who do travel should expect disruption because of the appalling weather conditions in France.
Ch Supt Matthew Nix, of Kent Police, said: "The welfare of motorists, some of who have remained in their cars for many hours, is our primary concern."
Stranded motorists will get hot drinks, snacks and blankets to help them cope.
Staff at the Channel Tunnel and the Port of Dover are working hard to clear the backlog, police added.
The train breakdowns coincided with strike action by Eurostar drivers in a 48-hour dispute over pay which began on Friday.
Around 70 members of the drivers' union Aslef are taking part in the industrial action.
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