There is also a risk that some rural communities could be cut off.
The Met Office said the mercury could dip between minus 4C (24.8F) and minus 6C (21.2F) going into Monday, with parts of the Midlands told to brace for minus 10C (14F).
Residents in Southampton, Hampshire were woken up at about 6.30am on Sunday by a loud thunderclap as snow began to fall in a rare event known as thundersnow.
When thunder and lightning mix with a heavy snowstorm it can cause loud claps of thundersnow.
BBC reporter Talia Slack said: “It knocked a vase of flowers over that was on my window ledge and a picture came off my bedroom wall. Never heard anything like it.”
Tom Morgan, a meteorologist at the Met Office, told the Southern Daily Echo: "A band of snow, sleet and some rain along the coast pushed across the whole of the Hampshire and it was quite heavy.
"We did have some thunderstorms as well and therefore we also this phenomenon called thundersnow, which is a thunderstorm that contains snow rather than rain."
Parts of the Midlands could record 6 in of snowfall by the end of the day, with the snow expected to remain on the ground well into next week.
Meteorologist Simon Partridge said: “The band of snow that came through overnight stalled over the Midlands and will then track its way back over south-east England.”
He added: “Our main focus is that it is going to be a really cold night, particularly across central and southern parts of the UK – so the whole of Northern Ireland, all of Wales, most of the southern half of England from the Midlands and southwards.”
Mr Partridge added: “Temperatures are expected to dip to between minus 4C (24.8F) and minus 6C (21.2F) quite widely tonight and where we get that snow lying in parts of the Midlands we could see one or two places where temperatures are as low as minus 10C (14F).”
Even in areas with lighter snowfall, a widespread frost is forecast, and conditions are expected to be hazardous including spots of ice on the roads.
It comes after the hashtag “Narnia” was trending on social media as snow briefly blanketed London.
Many took to social media to share pictures of heavy snowfall outside their homes as the capital was gripped by a cold snap from Iceland and the Arctic.
— Sadiq Khan (@SadiqKhan) January 24, 2021
But the snowfall was not without its challenges.
Buckinghamshire and Milton Keynes Fire and Rescue Service drafted in its Bobcat utility vehicle to clear snow at the Adams Park vaccination centre in High Wycombe so the rollout was not interrupted.
Elsewhere, the people of Seer Green in Buckinghamshire were called upon to rescue an ambulance stuck at the bottom of a hill in thick snow.
The South Central Ambulance Service tweeted: “A huge thank you to the people of Seer Green in South Bucks who came out in force to help one of our crews make it up a hill in thick snow at the bottom of Orchard Road/Bottom Lane earlier today.
“Great to see such community spirit and support for our NHS! Thank you guys!”
In Wales, four vaccination centres were forced to close because conditions were so treacherous.
The Cwm Taf Morgannwg health board said centres in Bridgend, Rhondda, Abercynon and Merthyr Tydfil would reopen on Monday, and that Sunday’s appointments would be rescheduled.
The board said no vaccines had been wasted, while 4x4s were being used to make sure doses still got to care homes over the course of Sunday.
There are five yellow weather warnings in place for snow and ice covering the southern part of England, eastern Scotland and Northern Ireland.
Icy patches on untreated roads and pavements are likely, with journeys by road and rail likely to be affected.
But the Met Office said by next week temperatures are due to jump back up.
Mr Partridge said by Wednesday the south of England would likely see between 10C (50F) and 12C (53.6F).
“It’s a bit of a rollercoaster from cold and wintry conditions to wet and windy ones,” Mr Partridge said.
“We are keeping an eye on rainfall totals because there are some areas that are very sensitive to rainfall and there is further possible flooding as we go through the second half of the week.”
Additional reporting by PA Media.