Prime Minister Andy Burnham said the UK has offered £5m to help the Nepalese government following the floods, saying it was a “very distressing and devastating situation”.
He had previously urged Britons in the region “to follow guidance from the local authorities and follow our travel advice”.
Speaking on Thursday, King Charles said he and the Queen were “heartbroken” and sent their “most profound sympathy” to those affected.
As rescue efforts continue, details of the missing are slowly emerging.
Fishtail Tours and Travels confirmed Leena Bector, from Slough, was among 27 travellers linked to the tour company who remain unaccounted for.
Her husband, Bhupesh Bector, told The Times: “I know that she’s in Nepal for sure, so even if they find her today or tomorrow, I need to be there.”
Essex nurse Rajendra Pudasaini said his relatives were “swept away” by the floods.
“My wife’s auntie and uncle, and their granddaughter and her husband are missing, and my godson as well,” he told PA Media.
“They’re gone. The speed the water came, they couldn’t be saved, they were just swept away.”
Sarada Simkhada, a senior nurse at Darent Valley Hospital in Kent, is also among the missing, according to a local councillor.
The Times said Simkhada was “following in the footsteps of thousands of Hindus this month in making the spiritual journey to Mount Kailash”.
Tatajana Phillips, from Folkestone in Kent, told the BBC she has not been able to contact her sister who was near the Nepal-Tibet border when devastating flash flooding hit.
She said the last known location of her sister Julija Jakovicka was in the border area an hour before the flash floods struck.
“Then there is no more news,” she told the BBC.
Phillips said her sister, a mother-of-two living in Germany, was in the country for a yoga and meditation retreat.
“We are terribly worried,” added Phillips’ husband Ben. “We just know where they were and that’s really tough.”
