It comes nearly a week after the disaster that hit both Nepal and neighbouring Tibet, killing more than 1,000 people, with more than 3,900 still missing.
A Nepali army spokesperson earlier said a British male was among those rescued, along with 118 Nepalese people, of whom 44 were female and 74 male.
Later on Tuesday, the Telegraph reported that the British man, Alastair Chambers, had told them he was not rescued and had travelled to the region to help with aid efforts.
The BBC has contacted the UK Foreign Office for comment.
It has been previously reported that 33 British nationals are missing in Nepal in the wake of the floods.
More than 600 are workers believed to be trapped in a vast network of mud-filled tunnels at hydropower sites along Trishuli River are among the thousands who are still missing.
Nepalese Prime Minister Balendra Shah said on Monday that 279 people had been rescued from the sites.
The rescue operation is being spearheaded by an international team made up of Chinese and Nepalese military personnel, while experts from India, Korea and Australia are also involved.
On Tuesday, the Nepalese Tourist Board said it had rescued 330 foreign nationals in total.
Saturday saw a rapid development team from the UK arrive in Nepal to provide support for Britons and their families.
The team will work alongside the British embassy and local authorities to support British nationals arriving in and leaving Nepal in the coming days and weeks.
It comes after Prime Minister Andy Burnham said the UK had 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".
The flood hit early on Wednesday in Rasuwa, just north of Nepal's capital Kathmandu.
Preliminary information suggested it was caused by an earthquake, but the US Geological Survey said additional analysis indicated "the seismic energy was instead generated by a landslide".
It said a magnitude 5.2 seismic event caused by a "glacial collapse and debris flow" occurred near the border at 08:37 local time (03:52GMT) on Wednesday.