Extra police are being deployed across Tier 4 in London and south-east England to stop people from travelling and ensure only essential journeys are made, the transport secretary has said.
Meanwhile, Police Scotland is to double its patrols on the border with England, after the first minister announced tougher coronavirus travel restrictions.
From Sunday morning, much of south-east England has been placed under tough new Tier 4 measures in a bid to stem the spread of a new and highly-transmissible Covid variant.
Under these new restrictions people are banned from mixing indoors and outdoors with others and retail, leisure and hospitality businesses all closed.
Travel into and out of Tier 4 is also banned, except for essential purposes.
ITV News Correspondent Rebecca Barry reports on the impact the restrictions willhave on some families already struggling
After Prime Minister Boris Johnson announced the strict new measures, which also prohibit the mixing of households on Christmas Day, travellers flocked to train stations to make their journeys before the ban came in.
The announcements prompted a rush to London's train stations and by 7pm on Saturday, there were no tickets available online from several London stations including Paddington, Kings Cross and Euston.
Footage posted on social media showed large crowds at St Pancras station waiting to board trains to Leeds.
Health Secretary Matt Hancock condemned the scenes as "totally irresponsible", while Labour said it was reckless to give people just a few hours notice of the change in plans.
In a statement, Transport Secretary Grant Shapps said it was “incredibly important” that people followed guidance, stayed at home and did not try to travel.
He added: “If you are in Tier 4, the law means you must stay at home and you cannot stay overnight away from home.
“Across the rest of the country, you must stay local.
“Follow the guidance and please do not come to a station unless you are permitted to travel.
“Extra BTP (British Transport Police) officers are being deployed to ensure only those who need to take essential journeys can travel safely.”
Explained: What are the new Covid-19 restrictions and which areas are in Tier 4?
His message was echoed in a statement from the government’s Christmas transport tsar, Sir Peter Hendy.
Sir Peter said: “At stations we will be deploying extra staff, announcements will make the law clear, and additional BTP officers are in place to ensure that only essential journeys take place.
“People considering driving should also stay at home or stay local. The new restrictions mean that people should not travel into or out of Tier 4 areas, and across the country you should stay local.
“You should play your part in tackling the spread of this virus.”
Meanwhile, Police Scotland's chief constable said “highly visible patrols” on roads will be used to “deter anyone who might be considering breaching the coronavirus travel restrictions”.
First Minister Nicola Sturgeon announced severe lockdown measures for Scotland on Saturday.
They included a “strict travel ban” preventing travel to or from other parts of the UK, which was put in place last month but was due to be removed over the Christmas period.
Some exceptions to the ban are allowed for essential purposes.
In a statement, Chief Con Iain Livingstone said it would not be “appropriate or proportionate for officers to establish checkpoints or roadblocks to simply enforce travel restrictions”.
But he added: “Today, I have authorised the doubling of our operational presence in the Border areas of Scotland.
“These highly visible patrols will be proactively deployed on our road networks to continue our operational activity to ensure drivers and vehicles are in a fit condition to drive.
“The patrols will also deter anyone who night be considering breaching the coronavirus travel restrictions.”
He said he expects roads to be “quieter than usual over the corning days”.
“We have been clear throughout this public health crisis that your police service is here to support our collective effort to combat coronavirus.
“Though the rules have changed often and, at times, quickly, officers and staff will continue with common sense, empathy and discretion to work with our fellow citizens to help keep everyone safe.
“It is the consent of the public from which policing in Scotland draws its legitimacy.
“As our communities expect, where officers encounter wilfull, persistent or flagrant breaches we will act decisively to enforce the law.”
Outside of Tier 4 areas, three households across the UK are allowed to meet indoors on Christmas Day, although the advice is to keep contact to a minimum.
Anyone who is going to meet up with others or who has already travelled to be with friends of family should reduce their contacts for the next few days to avoid spreading coronavirus, Public Health England’s Dr Susan Hopkins has said.
She told BBC One’s The Andrew Marr Show: “I understand people’s wish to get home to their families and loved ones that they may live with on a normal day-to-day basis and wanted to get out of London last night.
“I hope that when they go to wherever they are moving to they reduce their social contacts and don’t contact anyone outside their household for the next 10 days, as that will help minimise the risk of transmission to other parts of the country.”
Mayor of London Sadiq Khan said the crowded scenes were “a direct consequence of the chaotic way the announcement was made”.
He told BBC Breakfast: “I understand why people want to return to see their mums, dads, elderly relations, but I think it’s wrong.”
He warned Londoners that they may not realise they have the virus and could risk spreading it to relatives.
Mr Khan added: “We now have a vaccine being rolled out, you can see light at the end of the tunnel.
“How are you going to feel if you pass the virus on to an elderly relation, somebody you love, whose life could well be long and fruitful because of the vaccine, who may catch the virus and, God forbid, lose their life?”
On Saturday night travellers were told that social distancing “will not be possible” due to the volume of people on trains, and those that felt “uncomfortable” should not stay on board.