Over the weekend, some areas woke to two icy mornings, with the mercury dipping to a low of minus 2C (28.4F).
Overnight on Sunday, temperatures mostly stayed above freezing, with a touch of frost and sub-zero temperatures in a few isolated locations, such as Cairnwell in the Highlands of Scotland.
For the north west, Monday's rain will clear to give brighter and showery weather, with snow likely across northern hills.
It will be coldest on Thursday with occasional wintry showers possible, and we should expect some very frosty nights.
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Met Office forecaster Helen Roberts said that, despite the mild start to Monday, it will become increasingly cold as the week progresses.
She added: "A return to cold is the theme for this week - cold, breezy with a return of widespread overnight frost and wintry showers predominantly around the coastal fringes of the UK.
"Thursday is looking like it might be the coldest day and night of the week. We will potentially have some lying snow across the hills of Scotland and northern England and that always helps to keep temperatures down, so we could potentially see temperatures as low as minus 8C (17.6F), possibly minus 10C (14F), across parts of Scotland where there is lying snow by Thursday night.
"And even across England and Wales we could see minus 6C (21.2F) to minus 8C (17.6F) and some snow across hillier parts."
She also said there could be ice or snow warnings later in the week.