Forecasters have warned of "treacherous" conditions in parts of the country amid intense rainfall.
Surface water flooding could cause problems for motorists during Thursday morning's rush hour, the Met Office said.
Weather warnings are in place for parts of Scotland, north Wales and the north-east and north-west of England.
The Met Office tweeted: "Amber and yellow warnings are in force for Thursday morning, so conditions on the roads will be treacherous for some with surface water flooding and intense rainfall."
Dozens of flood warnings and alerts were in place across England on Wednesday night.
Rail users were hit by cancellations and delays on Wednesday as torrential rain struck England, Scotland and Wales.
Met Office meteorologist Luke Miall warned that the wet weather would continue to blight parts of the country on Thursday.
He said: "As this system pushes up from the south east through the course of the night, it will re-intensify and continue through much of Thursday."
Mr Miall said parts of south east Scotland could see up to 100mm of rain, with an amber alert in place warning of heavy downpours.
According to the Met Office, the wettest ever June for the UK as a whole was in 2012 when an average of 149mm of rain fell.
Mr Miall said this month's rainfall so far was "still a long way off" breaking that record.
He explained that following a dry summer and winter river levels across the country were low, meaning much of the current flooding was surface water flooding that could potentially retreat quickly.
But by the end of Thursday, flooding would increasingly be the consequence of cumulative rainfall, he added.
There are currently no Met Office weather warnings in place for Friday and the weekend, with conditions forecast to be calmer.
The weather is expected to be drier, warmer and sunnier, but with the risk of heavy and thundery showers in some places.