The Bureau of Meteorology warned that extreme weather, including rain, wind and snow, could lead to flooding and disruption of transport.
Eurostar trains to and from London were cancelled, as severe weather in the wake of storm Gerrit disrupted travel plans.
High-speed services between Ebbsfleet International, in Kent, and London St Pancras International are not expected to run today due to a tunnel sinking under the River Thames.
Eurostar, which operates services from London to Paris, Brussels and Amsterdam, said all 41 trains to and from the capital on Saturday had been cancelled.
The operator said he was "very sorry" after thousands of people were stranded at St Pancras and advised people not to travel to the station.
Simon Calder, travel editor at the Independent, told Sky News: "many desperate people are paying hundreds of pounds for flights, while others are planning to take the bus.
Newlyweds Christopher and Nicole Carrera were planning to spend New Year's Eve at Disneyland Paris, but their plans were thrown into chaos by the cancellation.
Mrs. Carrera, from New York, said: "We have been in London since Wednesday and we wanted to leave today because we were supposed to go to Disney Paris tomorrow for new year's Eve.
"So obviously those plans have been ruined because now we won't get to Paris tomorrow until about six in the evening. So we will take a walk around the city (Paris) tomorrow when we get there and finally arrive at our hotel. It's just one step". One of those things."
The flooding, which occurred in a tunnel near Ebbsfleet International, also disrupted South Eastern Railway trains, and Steve White, managing director of the operator, said that there is "no timetable" for when the problem will be resolved.
A spokesman for Thames Water said the flooding was believed to be caused by the fire-fighting system and not one of its pipes, although a technician had been sent to "provide support to control the flow of water".
Engineers working on the tunnel said the water level was falling, but warned that the volume of water in the tunnel was "unprecedented".
The operator said there had also been major disruption to Thameslink services across London and across the South East due to a "shortage of train crew" which will continue until Sunday.
Network Rail in Scotland said speed restrictions are in place on the West Highland lines until 9am on Sunday due to the forecast.
More weather warnings have been issued
The Met Office warned winds of up to 75mph could hit parts of southern England and Wales on Saturday, while northern Scotland could see "significant snowfall".
A yellow weather alert has been issued for winds in parts of the South-East, South-West, East Anglia and Wales from 11am on Saturday until 3am on New Year's Eve.
A separate yellow warning for rain has been issued for parts of Wales between 10am and 6pm on Saturday.
In Scotland, a yellow weather warning was issued for most of the country due to rain and snow until midnight.
The Environment Agency has issued 26 flood warnings, meaning flooding is expected, and almost 100 flood warnings, meaning flooding is likely, across England.
"A difficult day to travel"
Travel will be a "difficult day,"said meteorologist Craig Snell.
"It will be another unstable day. Heavy rain has fallen across the north-west of the country, with snow falling in the highlands of Scotland".
"Rain will move across the rest of the UK tonight.
"We are likely to see 50mph winds in Wales and southern England, with wind speeds in the most exposed areas reaching 65-75 mph.
"It is possible that some roads will be closed if the branches break off from the trees."
This comes after a large part of the UK was affected by storm Gerrit.
The Scottish and Southern Electricity Networks said they had restored electricity to almost 48 thousand homes since the storm hit.
In Wales, 36 thousand properties also suffered power outages after lightning struck the Ceredigion region.
And in Greater Manchester, residents of Stalybridge, Tameside and Carbrook are still recovering from a strange tornado that knocked down trees and damaged houses .
It is believed that this whirlwind was caused by a supercell thunderstorm.
