The chilly weekend continued on Sunday as the mercury dipped below zero and fog coated large parts of the country.
The agency's Alex Burkhill said a fog warning had been put in place over sections of the West Midlands and north-west England.
"It's been a very frosty start but through the bulk of the day it's going to be largely fine and largely sunny," the forecaster said.
Putting the sun in Sunday! ☀️
Lot's of sunshine today, though some lingering fog too pic.twitter.com/AsbKAV2lbM— Met Office (@metoffice)January 19, 2020
It would still be "quite chilly" with expected highs of 8C scattered across parts of England, Mr Burkhill said.
He added that there would be some rain for the Shetland Islands.
But there would also be plenty of sunshine across the country, the Met Office said.
A mid-range cold weather alert has been issued by Public Health England from 6pm on Sunday to 6pm on Tuesday and the organisation is urging people to prepare for cold weather conditions and look out for those most at risk.
Dr Owen Landeg, principal environmental public health scientist at PHE, said: "Below 18 degrees, changes to the body mean that the risk of strokes, heart attacks and chest infections increase so heating homes to this temperature is particularly important to stay well."
The cold snap comes after Storm Brendan swept across parts of the UK last weekend, causing road closures and rail disruption, as well as gales of up to 80mph.
It also marks a change from last month when meteorologists confirmed that a new UK maximum temperature record for late December was set in the Highlands.
— Met Office (@metoffice)January 19, 2020
A temperature of 18.7C (65.66F) was recorded at Achfary in Sutherland on December 28.
The reading was validated following a "rigorous verification process", the Met Office said.
Asked why temperatures have dropped, Met Office forecaster Mark Wilson said: "It's all to do with the pressure pattern and it also depends on how high or low the pressure is. Right now there is cold air sitting directly on top of the UK and there is high pressure coming from the north and the east."