Gusts of 40mph are expected to push in from the Irish sea, while up to 60mm of rain could fall in some parts — rising to 80mm in mountainous regions.
Three flood warnings and 26 flood alerts are in place across England on Monday, the bulk of which are in the southwest, particularly Cornwall.
There are also two flood warnings in place for Wales on Monday near the Wye estuary in Monmouthshire.
Luke Miall, a meteorologist at the Met Office, said: “There's a turbulent week of weather ahead; it is starting to look wetter and windier.
"Temperatures will hit 16C in London and the southeast, which is the average for this time of year, although it will be cool in areas of rain.
"Going into Tuesday the rain will start to push towards Wales the southwest of England, with most of the UK seeing rain at some point.
“The winds will be much stronger on Tuesday with heavier showers in Northern Ireland and Scotland.”
He said this was due to a spell of high pressure and air being dragged in from the Mediterranean.
Wednesday will see some warmer weather, with some areas reaching 18C, although rain is still expected for most.
Mr Miall said: “Unlike this week where the weather has been fairly static, next week will be changeable with the rain having the most impact.
“This is fairly typical for the time of year.”
Additional reporting by Press Association