Between 40-60mm of rain could fall in some parts of England, forecasters said, with up to 25mm expected widely.
Although it is too early to predict which exact areas will see the heaviest rain, the Met Office said southern parts of England are most likely to see “significant rainfall”.
“[The heavy rainfall] brings a risk of flooding and disruption, but the situation is uncertain, such that the likelihood of this across any given county is small,” forecasters said.
Grahame Madge, a spokesperson for the Met Office, said areas from the Isle of Wight up to the M4 are predicted to see the worst weather.
He added that there were no weather warnings in place for the rest of the week but forecasters have urged people to keep an eye out for more warnings as the unsettled weather is expected to continue.
After a brief lull on Tuesday, “intense showers” with the possibility of coastal gales are expected to return on Thursday and Friday.
However, it will be slightly warmer than average for the time of year, with much of England seeing temperatures in the mid-teens.
The southeast is forecast to see the warmest temperatures at 18C, while the north will see the coolest temperatures – between 11C and 12C.
Luke Miall, a Met Office meteorologist, said: “Looking ahead to next week, I’m afraid there is more rain on the way.”
“It will be dry on Tuesday though – we’ve got a ridge of high pressure pushing through, giving us the driest day of the week,” he added.
“And thereafter, further wet weather with showers likely as we head towards the end of the week.”