© Dan Kitwood/Getty ImagesWaves crash against the harbour wall in Newhaven, England.
Police searched for two people, one a canoeist, feared to have fallen into the swollen River Taff in and around Cardiff while a woman was pulled to safety from the Ely, another river in the Welsh capital.
Campers and caravaners were rescued by firefighters from sites in south-west Wales while premises were damaged by flood water and falling trees, and rail lines and roads were blocked.
The Met Office said a number of areas across Wales and the Midlands were hit by record-high wind speeds for August.
Gusts of 68mph were recorded at Pembrey Sands in south-west Wales, 52mph at Shobdon in Herefordshire and 49mph at Pershore in Worcestershire - all August highs for these locations. The wind was even stronger off the Isle of Wight, with gusts of 73-78mph.
The Met Office issued an amber warning for very strong winds across most of Wales and central England between 2pm and 10pm on Tuesday. It said flying debris was likely and could lead to injury or danger to life. It also warned that large waves posed a danger to people on the coast.
The chief meteorologist, Steve Ramsdale, said: "Wind speeds this strong are unusual during August and may come as a surprise to people spending time outdoors trying to catch the last few days of summer."
An Environment Agency gauge recorded 86mm of rain in the Lake District and 74mm in Mid Glamorgan, south Wales.
South Wales police were involved in two separate searches of the Taff on Tuesday. A spokeswoman said emergency services were searching the river in Cardiff after reports someone entered the water near the Principality Stadium shortly before 8.40am, while a search was under way in Taff's Well north of the city after reports of a canoeist having capsized.
A woman was also rescued at the Ely in Leckwith, Cardiff. Penarth lifeboat station said it was believed the woman went into the river to help a dog that was rescued with her.
"Although obviously cold and wet, both appeared in good spirits and were taken for medical checks," a spokesperson said.
In Cardiff, a restauranteur was inside the premises when a tree crashed on to the building. Mamun Miah said he was making phone calls in the newly refurbished Lake Spice Curry House when the tree fell. He was unhurt.
Fire crews rescued nine holidaymakers and two dogs from a flooded campsite, Lakeside, in the town of St Clears, Carmarthenshire, after river levels rose in the area. All campers were safe and taken to alternative accommodation.
Crews also gave medical treatment to one man and evacuated 30 other people from a flooded caravan site in Narberth, Pembrokeshire.
A number of homes in south Wales were hit by flooding in Llanelli and Neath. The M48 bridge across the River Severn was closed in both directions due to the wind speeds while power cuts affected hundreds of homes.
People were rescued from their homes in the seaside town of Newcastle, County Down, Northern Ireland, after a river burst its banks. Up to 300 homes were affected and streets left under around a metre of water.
Trees blocked a number of rail lines and roads including the A30 in Cornwall. RAC spokesman Rod Dennis said: "Until the middle of Wednesday, drivers need to brace themselves for some very unpleasant conditions on the roads."
By late afternoon on Tuesday the Environment Agency had issued 26 flood alerts for the Midlands and the north of England. There were 20 flood alerts for Wales and 11 for Scotland.
The Met Office said Storm Francis would clear to the east of the UK by Wednesday lunchtime. It said there should be sunshine and scattered showers over the bank holiday weekend before further unsettled weather moves in from Tuesday next week.
Comment: Less than a week ago Storm Ellen caused widespread damage across Ireland and parts of the UK.