Warnings are in place for parts of Kent and Sussex between 10am and 5pm on Monday while another storm warning has been issued for large parts of the Midlands and northern England between 9am on Tuesday and 6am on Wednesday.
A Met Office spokesman said: “Going forward, there’s some more thunderstorms and intense downpours in the forecast, with a yellow weather warning for thunderstorms currently active until 5pm today in the far South East.
“The current dominant weather pattern of the UK is set to be a spell of low pressure, bringing with it some more persistent rain from Tuesday and into Wednesday, with some slow moving heavy rain expected over Scotland on Wednesday in particular.”
The rainfall on Sunday caused flooding across parts of London, as well as major disruption to the transport network.
There is also a yellow thunderstorm warning in place for most of Scotland between 12 noon and midnight on Tuesday.
Yellow rain warnings also remain in place for all of Wednesday and Thursday morning.