Heavier rain, sunshine and showers are forecast for the week ahead but temperatures could hit the mid-twenties by next weekend.
Rain is forecast on Monday and Thursday, with a mix of sunshine and showers through the rest of the working week, Met Office forecaster Craig Snell said.
The weather is expected to settle by the weekend and “could potentially feel markedly warmer”, he added.
Mr Snell said: “There are hints as we go into the weekend we may well see a slight warming up.
“It’s hinting at 24C for London on Saturday, at least into the low twenties, maybe mid-twenties across the southeast.”
A band of rain will spread east on Monday, then sunshine and scattered showers are forecast on Tuesday and Wednesday, Mr Snell said.
Thursday will see another band of rain spread across the country during the day, and on Friday there will be sunshine and showers.
By the weekend, higher pressure will build over the south, but it may take longer before it settles down in the north.
“After quite a bit of a changeable week with some potential cold periods, when it settles down, it could potentially feel markedly warmer, even reaching 24C or 25C,” said Mr Snell.
Temperatures in the working week will range between 17C and 18C in the south and 15-16C in the north, while over the weekend they are expected to reach the low twenties in the south, with the potential for 24C or 25C in the southeast, and in the high teens in the north, the forecaster said.
The Met Office will be keeping an eye on the bands of rain arriving on Monday and Thursday, but it is not currently expecting to issue any weather warnings.