The prime minister and the Foreign Office in the UK have urged people to follow local guidance and remain alert to the changing situation, as officials in Nepal warn of a possible secondary flood risk near the Bhote Koshi river.
The Foreign Office added it was working closely with Nepalese authorities.
A British woman from Slough, Leena Bector, has been confirmed by Fishtail Tours and Travels as missing. Her husband, Bhupesh Bector, told the Times he is flying out to the country.
“I know that she’s in Nepal for sure, so even if they find her today or tomorrow, I need to be there,” he said.
British resident Pramod Pudel, who lives in East Sussex but is originally from Nepal, told Radio Sussex on Thursday that “nothing remains” where his family lives and he is flying back to search for his wife, mother, brother and uncle.
“It’s a very, very difficult time for me and for my family and my country at this moment, but obviously I have to go and see what’s happening there,” he said.
“A lot of people are missing and there is no information regarding who is missing, where they are. Nobody can contact each other and all the bridges are broken, so you can’t cross the land.
“There’s no power, no electricity, so I can’t contact anyone, so it’s a very difficult time not knowing what’s happening.”
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.”
Meanwhile, a Nepalese man living in Aberdeen Barun Lamichhane, 26, told Scotland News his brother, uncle and cousin all died in the disaster – but his mother, father and grandmother managed to escape.
Lamichhane said they got away by “crawling like a baby” into the hillside.
Other families are waiting for news, including Tatajana Phillips, from Folkestone in Kent, who said the last known location of her sister Julija Jakovicka was in the border area an hour before the flash floods struck.
“We are really hoping that people hear us and try to find and locate [my sister]”.
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.”