Monday will see outbreaks of rain across many northern parts. However, further south will remain mainly dry with some brightness particularly through the morning. The rain will start across western parts of Scotland and Northern Ireland.
Eastern Scotland will be generally dry along with northeast England.
Many central and southern parts will experience a similar start with one or two isolated showers towards the south and west.
Met Office Meteorologist Mark Wilson said: “Through the day that cloud will continue to thicken across many northern areas.
“Outbreaks of rain will spread in across Scotland, northern England and Northern Ireland.
“The rain always heavy and more persistent towards the west of Scotland.
“Further towards the east with high ground will be somewhat drier into the afternoon with the odd limited brighter break.”
Across central and southern parts of England and Wales it will turn cloudy into the afternoon.
There will be little change heading into Monday evening.
Overnight will see further outbreaks of rain come across Scotland, northwest England and Northern Ireland.
However, it will turn a little bit drier across the very far north.
Further south across much of England it will generally dry with variable amounts of cloud and no problems with temperatures across the country.
Mr Wilson continued: “As we look ahead into the bigger picture for Tuesday, there will be some further rain around.
“But it will mainly be in the northwest, particularly across western Scotland and northwest England.
“The best of the dry and brighter weather will be across the south and east.
“In the sunshine, it should feel fairly warm.
“But it will stay rather changeable for much of this week.”
No weather warnings have been issued for the rain across the UK.