The AA expected to be called to more than 20,000 motoring breakdowns by the end of Monday.
"The cold weather has combined with the return to work and schools making it a very busy day - most of the extra workload is home starts with flat batteries being the most common call-out," an AA spokesman said.
On Monday, motoring organisations reported a 100% increase in the number of call-outs they had to go to.
Gritters are out on roads across the UK spreading thousands of tonnes of salt overnight.
Forecasters say it is expected to get even colder on Monday night, with temperatures hitting -10C in some places.
But that is still a long way off the record low of -27C (-16.6F) in northern Scotland 14 years ago.
The Met Office has issued an advance weather warning for parts of south-east England, with icy conditions expected.
The Welsh Valleys, the West Midlands and north-west England will also be badly affected, the BBC Weather Centre said.
Pensioners have been advised to take extra precautions to stay warm during the icy spell.
Age Concern's director general Gordon Lishman said: "With predictions of more snow and freezing temperatures this week we are urging vulnerable older people, who are more susceptible to the cold, to take extra precautions to stay warm and keep active."
Some £5bn of benefits were still going unclaimed despite some of the poorest pensioners struggling to afford essentials such as food and heating, he added.
The government said 2.5 million cold weather payments had already been made.
The current cold period is expected to ease later in the week.
The BBC Weather Centre said Scotland would experience a milder day on Tuesday, with the cloudier weather then spreading to the rest of the UK.
"It will get less cold," said Mr Gibbs. "By the end of the week we will reach 4C (39.2F) to 6C (42.8) - but still below average for most of us."
Pensioners worried about high energy bills can call Age Concern's free helpline on 0800 00 99 66 for advice.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.