Last month was the wettest June the UK had seen since detailed records began in 1914.
Water is still being pumped out in Hull
The Met Office confirmed that 134.5mm (5.3in) of rain fell across the four countries. The average June rainfall in the UK is 72.6mm (3in).
A new record was also set for England, with 140.2mm (5.5in) of rain.
Flood victims in Hull - where more than 10,000 homes were evacuated - may not
be able to return home for up to a year, the city council has said.
More heavy downpours are expected across the UK as the clear-up continues in areas hit by severe flooding.
In Hull an additional 700 council staff have been taken off their normal duties to join local area teams helping the thousands displaced by flooding.
The authority said its latest figures showed 16,064 homes had been affected and that more than 5,000 had already been visited to assess needs.
Some £18m has been earmarked for repairs to the affected homes, but the council said the cost of the floods could reach £200m.
It feared some schools would not re-open until as late as December or January, although it was awaiting full inspection reports, it added.
Heavy showers and isolated thunderstorms were expected in the northern half of Scotland and parts of northern England, said the BBC Weather Centre.
The Environment Agency still has 10 flood warnings in force in Anglia, north-east and north-west England, the Midlands and Wales.
The warning means flooding of homes and businesses can be "expected".
In Doncaster, the council said 181 people from flood-hit areas remained in temporary accommodation.
But residents in Arksey, Almholme and Bentley were allowed to return home after the Environment Agency downgraded the severe flood warnings throughout the area.
Bentley and Arksey have been completely cleared of water.
Assistant Chief Constable Mark Whyman of South Yorkshire Police said his officers had responded to thousands of emergency calls during the operation and evacuated about 3,000 people from the Doncaster area.
At Toll Bar - one of the worst-hit areas - 24 high volume pumps brought in from across the country continue to pump away 14 million litres of water an hour.
The water levels are falling slowly and the operation is expected to take another three to four days, the council said.
Prince Charles saw Toll Bar's flooding by boat
Earlier on Wednesday Prince Charles visited Toll Bar.
He saw some of the devastation suffered by hundreds of homes in the village, which was first hit by flooding a week ago.
And he entertained onlookers by sitting in an inflatable boat to be rowed along the deserted high street, which is still under up to 4ft (1.2m) of water.
Joe Giacomelli, of the Environment Agency, said Toll Bar was the site of the agency's last severe weather warning, which was lifted on Tuesday.
He said where the ground was saturated, heavy rainfall was likely to run straight into rivers, raising water levels.
Parts of south London were hit by flash floods on Tuesday following a massive storm that swept across the South East.
Fire crews spent more than eight hours pumping water from dozens of homes hit by torrential rain in Kent. Minster, on the Isle of Sheppey, bore the brunt of the downpours.
A mother and daughter are recovering in hospital after being struck by a bolt of lightning which killed their dog while out walking in Norfolk.