The Met Office said a cold front moving southwards is expected to bring some showers and winds while cold air coming from the north is going to lead to a drop in temperatures.
Scotland is predicted to have a mixture of single-figure temperatures and low double figures – 9C (48.2F) to 11C (51.8F) – from Monday onwards while England, Wales and Northern Ireland are expected to see highs of 12C (53.6F) and 13C (55.4F).
Sunday is expected to be warmer, with central and southern parts of England dry with sunny spells while the north and Wales will be cloudy and overcast.
Scotland and Northern Ireland, meanwhile, are predicted to have heavy rain and cloud on Sunday before the cold front moves in.
Alex Burkill, a meteorologist at the Met Office, said: “We’ve got a cold front that is pushing its way southwards as we go through to tomorrow, more so later tomorrow and into Monday.
“It will bring some rain and some strong winds, probably the first significant strong winds of the season so far particularly for Scotland, but the bigger talking point being the cold air that’s going to come down from the north behind it. So, temperatures are going to take a bit of a drop.
“I think Sunday night into Monday is going to be a bit chilly for some but because of the cloud, the rain, the strong winds, temperatures won’t drop too much. I think it’s going to be from Monday onwards when we’re going to see the real cooler feel.”
Mr Burkill added that while southern and coastal parts of England on Monday could see highs of 16C (60.8F) and 17C (62.6F), Scotland is expected to see a maximum of 8C (46.4F) or 9C.
Temperatures on Tuesday are believed to fall again, with England seeing an average of 11C or 12C, while Wales and Northern Ireland could see 12C on average.
Scotland will see a slight increase in temperatures that day, with a maximum of 11C.
Monday is predicted to have a rainy start for the southern parts of England and northern parts of Scotland, with the south and central England switching to cloudy with sunny spells as the day progresses.
Wales, Northern Ireland and the rest of England and Scotland are expected to remain cloudy for the day.
Tuesday is predicted to be cloudy and overcast for the whole of the UK, with some sunny spells in the late morning and early afternoon across the east and north-east parts of Scotland and England.
Rain is predicted for Wales and the north-west and south-west of England later on Tuesday.