The Met Office has issued an 18-hour long yellow warning, running from midnight until 6pm on Sunday, covering Scotland and most of northern, eastern and south east England.
Forecasters warned that heavy rain could cause disruption on the roads, as well as to train and bus services.
Flooding is likely to affect a few homes and business, while some communities may be cut off by flooded roads, the Met Office said.
Thunderstorms swept across London, the south of England, Wales and the Midlands on Tuesday, with some areas hit by a week’s rain in just an hour.
Met Office meteorologist Alex Burkill said Sunday’s yellow warning was triggered by rain pushing eastwards across the UK.
“It’s going to stall and linger across northern and eastern parts of the UK tomorrow,” he said on Saturday evening.
Mr Burkill said the highest rainfall totals were expected in Scotland and northern England, but the highest rainfall rate is likely to be seen in Lincolnshire and East Anglia.
He explained: “That’s where we could see quite a lot of rain in a few hours, whereas further north it will be longer but not as intense.”
By contrast, Northern Ireland, Wales and south west England are due to see sunshine on Sunday, with some heavy showers.
Beyond the weekend, further rain is forecast for Monday followed by a showery and blustery week of weather – with average to milder temperatures, Mr Burkill said.
He said the unsettled weather theme will continue into November, with temperatures dropping below average “but not extremely cold”.