Video report by ITV News Correspondent Stacey Foster
Yvonne Booth, 55, from the Great Barr area of Birmingham, went missing near Tenbury in Worcestershire on Sunday.
Her body was recovered on Monday following a police search.
A statement from her family, released by West Mercia Police, said: "Yvonne is a very much loved member of our family and we are all devastated by this news."
"We appreciate the continued support from the emergency services. We would like to ask for our privacy at this time."
Storm Dennis battered the country with winds of more than 90mph over the weekend, while more than a month's worth of rain fell in 48 hours in places.
The Environment Agency (EA) warned torrential rain from Storm Dennis has swelled rivers to "exceptional" levels in parts of Britain.
It warned the flood risk continues, with further heavy rain forecast in the north of England for Wednesday and Thursday, possibly falling on already flooded areas.
Communities across the country are counting the cost of the weekend's storm which has left more than 400 properties flooded.
Among the worst affected areas are south Wales, Herefordshire, Worcestershire and Shropshire where major incidents were declared.
Home have been evacuated in Hereford and Monmouth as the River Wye recorded its highest ever level.
The water level is predicted to rise yet further and hit 7.2 metres when the peak passes through the Monmouthshire county town between 3am and 7am on Tuesday.
Residents living in areas at immediate risk have been evacuated and other properties nearby have been provided with sandbags and support.
Residents in Upton upon Severn and Uckinghall, in Worcestershire, were also advised to evacuate.
The aftermath of the storm caused transport disruption on Monday, as train lines and roads were blocked by flooding and fallen trees.
The AA said nationally it had attended more than 400 vehicles stuck in water or mud over the weekend, more than double that under Storm Ciara a week ago.
Hereford residents were advised that flooding could trigger periodic power cuts and some roads were closed.
Speaking in Worcester, the EA's David Throup, West Midlands environment manager, told Sky News: "I think it's peaking now in Hereford, the levels that you've got there are truly exceptional levels, they are the highest levels we've ever recorded on the River Wye and those records go back 200 years."
He added: "Here in Worcester, the River Severn is also at a level that is similar to the big floods in 2007."
As of 8.30pm on Monday, seven severe "danger to life" flood warnings from the EA were in place for the River Trent at Burton upon Trent; the River Wye at Blackmarstone in Hereford, and at Hampton Bishop; the River Severn at Uckinghall and at New Street and Waterside in Upton upon Severn; and the River Lugg at Hampton Bishop.
Natural Resources Wales issued two severe flood warnings for the River Wye at Monmouth, with the water level expected to peak between 3am and 7am on Tuesday.
The EA's executive director of flood and coastal risk management, John Curtin, tweeted that 420 properties were flooded by Storm Dennis and 18,500 protected, with both figures expected to rise.
He indicated that 800 properties were flooded by Storm Ciara.
Locals in the inundated area around Hereford described "devastating" flood scenes that struck roads, a business park, the railway line and homes.
Greg Smith, who took drone images of the flooding, said: "I've never seen anything like this."
Meanwhile, residents living near Eastham Bridge in Worcestershire described 48 hours of chaos as they lost count of the number of vehicles - including a fire engine and a petrol tanker - caught in floodwaters.
Over in South Wales, one of the worst-hit areas was the village of Nantgarw, near Cardiff, where entire streets were left underwater from the early hours of Sunday morning.
Jeanette and Rachel Cox had a "terrifying" evacuation from their home in Oxford Street after waking at 4am to the floodwater.
"Everything downstairs has completely gone," said 68-year-old Ms Cox, who was only able recover a wedding day photo of her with husband Bill, who died from cancer in 2009.
ITV News Correspondent Sejal Karia looks at the impact of the flooding in Wales
Visiting the flooded village of Trehafod, near Pontypridd, Plaid Cymru leader Adam Price criticised the Welsh Government's level of investment in flood defences, saying the weekend's events were a "wake-up call".
Natural Resources Wales said provisional data indicated the River Taff at Pontypridd had reached its highest level for over 40 years.
Youth climate strikers said they had to cancel their first ever national conference, with delegates coming from across the UK, due to serious flooding in Staffordshire.
The Prime Minister resisted calls to chair a meeting of the Government's emergency committee, Cobra, to tackle the flooding crisis, despite criticism from the Labour Party.
Luke Pollard, shadow environment secretary, said it was a "disgrace" that Boris Johnson had "refused" to visit affected communities.
Asked why Mr Johnson was not making personal visits, a Number 10 spokesman said he was receiving regular updates and that Environment Secretary George Eustice was leading on the issue.
Mr Eustice defended the Government's response, saying it was not possible to protect every house from flooding and pointed to £4 billion of funding committed to flood defences in the next five years.
Meanwhile, local authorities hit by flooding will be able to recoup some of their costs via emergency financial assistance available through the Bellwin Scheme, the Government said.
A record number of flood warnings and alerts, more than 600, were issued by the EA across England on Sunday, with this falling to below 500 on Monday afternoon.
The Met Office has issued two yellow weather warnings for snow and ice over parts of Scotland from 6pm on Monday, with further warnings of persistent rain in Wales for Wednesday and Thursday.
Footage of a landslide in Tylorstown, Rhondda Cynon Taf, south Wales on Sunday morning: