A month’s worth of rain in 24 hours is also forecast to hit north Wales and north-west England, falling on ground that is already saturated.
Eight rivers have reached record levels in recent days, the Environment Agency (EA) said.
Nearly 120 flood warnings remain in place across the country.
The EA said there is a “heightened flood risk” across the Midlands, with six severe warnings – meaning there is a danger to life – still in place near the Welsh border around the Rivers Lugg, Severn and Wye.
Dave Throup, the EA’s manager for Hereford and Worcestershire, said the Wye flooding was over half a metre bigger than anything for 110 years.
“It’s getting scary folks,” he said on Twitter, adding that “what I’ve seen over the last few days isn’t normal. It isn’t even the new normal. It’s going to get worse. We need to adapt and respond. And fast.”
He said that he was “so sorry for everyone whose life has been turned upside down”.
Hundreds of people have been evacuated from their homes in the worst-affected areas, which include south Wales, Herefordshire, Worcestershire and Shropshire.
Meanwhile, Prime Minister Boris Johnson has faced criticism from opposition parties for not visiting flood-hit communities.
Labour leader Jeremy Corbyn said he was showing his “true colours by his absence”, adding that the prime minister was sending a “clear message” by not convening the government’s emergency committee, Cobra.
Plaid Cymru leader Adam Price also questioned why Mr Johnson had not convened Cobra, the government’s emergency response committee.
On Wednesday, business minister Nadhim Zahawi told Sky News that the prime minister was focused on getting “money out the door” to businesses and local authorities in affected communities.
“He wants to help people by getting funding to them,” Mr Zahawi said.
Environment Secretary George Eustice said the government was investing £2.6bn in flood defences.
Yellow warnings for rain will remain in place in south and north-west Wales until 14:00 GMT on Thursday, with the Met Office saying they could see 50-60mm (2in) and 70-100mm (4in) of rain respectively.
Another yellow warning for rain covers part of north-west England until 15:00 GMT on Thursday, where up to 100mm could fall.
“In the worst case scenario, we could see a month’s worth of rain,” said the Met Office’s Craig Snell.
He said as the ground was saturated due to persistent, heavy rainfall, the rivers were less likely to be able to cope with further rain.
Rain fell heavily across northern and western parts of Britain overnight, according to the Met Office.
The village of Capel Curig in north Wales received 54mm of rain in 24 hours – more than half the average rain for the whole of February.
Other yellow weather warnings for rain are in place for:
Southern Scotland and the Scottish borders until 11:00 GMT on Thursday;
Western and south Scotland from 06:00 GMT until 21:00 GMT on Friday;
Yorkshire from 12:00 GMT on Friday until 6:00 GMT on Saturday;
A yellow warning for wind for north-east England, southern Scotland and Yorkshire are in place for 12 hours from 8:00 GMT on Friday.
According to the EA, England has already received 141% of its average February rainfall so far this month.
River levels in the Colne, Ribble, Calder, Aire, Trent, Severn, Wye, Lugg, and Derwent all set new records in recent days, it added.
Meanwhile, charity the RSPCA said animal rescue officers had been called out more than 200 times in the past 72 hours – including for “dramatic rescues” of 60 sheep, horses, a swan and chickens.
Actor Michael Sheen, from Neath Port Talbot, has launched a crowdfunding campaign to help flooded communities in south Wales.
“The devastation that Storm Dennis has left behind is very real and thousands of people across the UK have lost everything,” said Sheen, 51.