Rescue teams in Nepal are searching for at least 33 British nationals who are among those missing after flash floods ravaged its border with Tibet, killing at least 353 people.

Nearly 1,400 people are missing, most of them tourists, authorities have said, after a glacier collapse triggered floods that roared down valleys and razed entire villages.

The tour company Kailash Journeys confirmed it had not been able to account for seven UK nationals – five women and two men aged between 18 and 55 – travelling with it.

Another tour operator, the Trekkers’ Society, said among the British citizens who had been completing one of its tours to the sacred Hindu site of Mount Kailash were four males aged 14, 50, 50 and 54 and five women aged 40, 46, 50, 50 and 53.

The tour operator Alpine Eco Trek said a 13-year-old girl was among the missing British nationals and two Irish citizens were also missing. They were on a nine-day tour to Mount Kailash and crossing into Tibet from Nepal when they became trapped at the border as the flash floods struck.

Other missing British nationals with Alpine Eco Trek are three men aged 65, 64 and 52 and seven women aged 44, 47, 51, 60, 63, 63 and 65, according to travel logs.

The tour company Himalayan Glacier US told the BBC they had lost contact with a group of 47 guests, including two British citizens, who were en route to Mount Kailash. Fishtail Tours, a Nepali travel agency, said one British person was missing.

Andy Burnham has pledged an initial £5m in UK government support and offered to send emergency responders and rescue support to assist Nepal’s disaster response efforts. Speaking to journalists during a visit to south Wales, he said: “It’s a devastating picture that is emerging from what has happened in Nepal. Scenes that we’ve never seen the like before, I don’t think, certainly the scale of the devastation.

“So there is immediate action being taken. We are deploying consular support staff to the region so that British nationals will be able to access support 24/7. Obviously there are a number of British nationals who currently are thought to be missing and we’ll be providing all the support we can to their families in what is a very distressing and devastating situation.”

In a statement, he added: “In the past, Nepal has been there for Britain in our hour of need, and we will be there for Nepal in its hour of need right now.”

The president of the Nepal Centre for Disaster Management, Bishal Nath Upreti, told BBC Radio 4’s Today programme that the flash floods were like a “tsunami from the sky”. He said: “It’s a huge debris, and in fact, after the 2015 earthquake, this is one of the largest disasters that we have [had] in Nepal.”

He added: “It was such a huge amount of water. You can imagine it is 20m cubic metres excess water on the river … Villages and villages along the almost 40 to 50 kilometres were completely wiped out.”

The Nepal tourism board said on Wednesday that 33 UK citizens were among the foreign nationals unaccounted for. At least three people had died in Tibet, according to China’s state broadcaster CCTV, while the Xinhua news agency said 558 people were unaccounted for in the region.

Rescuers are racing to locate people missing in the mountainous Rasuwa region, which borders China’s autonomous region of Tibet and is popular with trekkers and pilgrims.

Pramod Poudel, from Uckfield, East Sussex, told the BBC that his wife, parents, brother and uncle had been caught in flash flooding. He said he would fly to Nepal on Thursday night to try to make contact with them.

Poudel said: “I guess there is no power so they can’t charge their phones – to be honest, it’s a very hard and difficult time at the moment.”

In an emotional interview, he said: “I have seen pictures of where my home town used to be … and there is nothing there now.”

The UK government minister Pat McFadden told Times Radio the picture was “not completely clear yet”, with “many, many more” people understood to be missing than those reported by the Nepalese authorities, and no clear figures from China yet.

He said: “In terms of missing Britons, my colleague the foreign secretary, Ed Miliband, has posted on social media phone numbers that people can call for further information.

“But it’s a fast-moving picture. We don’t have a full picture yet of the numbers missing.”

The Foreign, Commonwealth and Development Office said it was “deeply saddened by the loss of life and devastation caused by the floods in Nepal”. It added: “British nationals in Nepal should follow local authority advice and exercise caution while travelling. For consular assistance call (+44) (0)207 008 5000 or (+977) (0)14237100.”