The Met Office said downpours would likely cause flooding on roads and make journey times longer, with flooding of homes and businesses also possible.
Heavy rain could cause travel chaos across the weekend as it coincides with a strike by train drivers on Saturday.
The Met Office has issued yellow weather warnings for southern England and southern Wales on Saturday and Sunday. Parts of Scotland are under a yellow weather warning on Saturday.
It said downpours would likely cause flooding on roads and make journey times longer, with flooding of homes and businesses also possible.
Four flood warnings and 56 flood alerts have been issued in England.
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The weather warnings on Saturday coincide with train drivers belonging to the Aslef union striking in a long-running dispute over pay, impacting 11 operators.
Companies where no services are expected to run include Avanti West Coast, CrossCountry, Chiltern and East Midlands, while others including Great Western and Greater Anglia say services will be extremely limited.