Flood warnings are in place in much of the Southwest around Wolverhampton, Leeds, Norwich and Eastbourne.
Frost and fog are set for the end of the week, with freezing fog rolling across England and Wales, a spokesman for The Met Office said.
Forecasters said: “We’ve seen an average start to the month in terms of precipitation. We’re running 30 percent of the average rainfall – we usually expect that to be at that value.
“But high-pressure building and fog are the main problem.
“It looks very good in the middle of the week, and Wednesday can be quite sunny – but there is a risk of overcast snow on Thursdays and Fridays.
“So it has low temperatures in the ice, and it can cause some disruption to travel and aviation, so there may be some disturbances at airports, for example.
“But there’s no snow or particularly disruptive wind.”