The Met Office has issued a yellow weather warning for parts of the north of England, Midlands, Scotland and Wales on Wednesday.
The forecaster warned there was a small chance homes and businesses could be flooded and the weather could lead to difficult driving conditions and road closures.
Flood alert warnings were issued for some areas in England, Wales and Scotland.
The Environment Agency issued 44 flood alerts for England, advising flooding was possible, and five flood warnings, which mean flooding is expected and immediate action is needed.
This week has seen showers and thunderstorms in southern and eastern parts of England, with a persistent band of rain edging north and west as the week has continued.
Met Office weather warnings are in place until Thursday.
In Wales, people were advised not to travel unless it was essential.
Transport for Wales tweeted: "Continued heavy rain during today means that travel to and from your desired destination cannot be guaranteed."
National Rail reported that heavy rain and flooding was affecting services in the North West and trains could be cancelled or delayed as a result up until 1pm.
Routes affected include the Merseyrail service between Hamilton Square and Ellesmere Port and Chester, as well as Transport for Wales services between Aberystwyth, Chester, Crewe and Shrewsbury.
Virgin Trains between Llandudno Junction and Crewe and Chester were also said to be affected.
North Wales Police tweeted about road closures in the area.
A message on the force Twitter account said: "Good Morning, weather and road conditions are atrocious.
"Please slow down wherever you may be going.
"Assess the need for your journey, drive to the conditions and your driving ability. Please DO NOT ignore any road closure signs. Think Safety."
Met Office meteorologist Bonnie Diamond said parts of the country could see 0.8in-1.6in (20mm-40mm) of rain on Wednesday, with 2in-3.2in (50mm-80mm falling on higher ground.
She said the heaviest rainfall was expected to be in the Teesside area, much of it overnight, with the weather warning extending into Thursday.
She said: "Anywhere within the warning area there is a risk that, with persistent rainfall, there could be a localised impact in terms of flooding.
"Tomorrow unfortunately is another wet day."
Weather warnings for rain in eastern England and Wales on Thursday afternoon are expected to be issued.
Going into the weekend, the wind direction is expected to change, meaning less heavy and persistent rain, although the weather will still be unsettled with some showers expected, Ms Diamond said.
Flood warnings are in place for Maghull in Merseyside, Winsford in Cheshire, and three areas of Lincolnshire.
Weather warnings are in place across the UK as torrential rain continues for another day.