Dozens of British and Irish people have still not been traced following Saturday's devastating earthquake.
The Red Cross had said 90 Britons were missing, but 30 have been located and the UK Foreign Office said it was not aware of any deaths or injuries.
The UK's leading aid agencies have announced a joint appeal to raise money to help survivors.
More than 4,300 people died and almost 8,000 were injured in the quake.
Eighteen of the dead were killed in avalanches on Mount Everest.
The RAF C-17 flight, commissioned by the Department for International Development, left RAF Brize Norton, Oxfordshire, carrying more than 1,100 shelter kits.
The plane also contains more than 1,700 solar lanterns to help families who have had to sleep outside because their homes have been demolished or through fear of further aftershocks.
BBC correspondent Jon Kay said it took ground crew nearly six hours to load the 30 tonnes of emergency supplies.
About 15 sombre-faced Gurkhas, who are synonymous with Nepal, were among the troops who had left on the flight, he added.
An RAF Hercules aircraft is also expected to leave the UK on Tuesday carrying additional kit.
The International Committee of the Red Cross had released a list of 90 missing British and Irish people, but the BBC understands more than 30 have since been accounted for.
However, there could still be additional missing Britons not on the Red Cross list.
Patchy mobile telephone and email communications have made it difficult to locate people.
The Disasters Emergency Committee, comprising the UK's leading aid agencies, has also announced an appeal to raise money to help survivors.
The appeal is to launch on the BBC, ITV, Channel 4, Channel 5 and Sky on Tuesday. A donation line and website has already opened ahead of the broadcasts.
The UK government has also promised to match the first £5m of public donations.
The government has already given £5m to help people affected by the earthquake. It said it had released £3m to address immediate needs and £2m would be given to the Red Cross.
Foreign Secretary Philip Hammond said "we would expect there to be several hundred British nationals in Nepal".
"British embassy staff have helped over 200 British nationals who've presented at the embassy directly," he said.
The Foreign Office said teams had also been scouring hospitals, hotels and areas popular with tourists looking for Britons that might need help.
A spokesman said: "The situation on the ground is highly challenging. Basic telephone communication and infrastructure are severely disrupted."
The UK Foreign Office has released an emergency number - +44 (0) 207 008 0000 - for people worried about loved ones who may have been in the area at the time.
It advises against all but essential travel to Nepal.
Britons in a safe place have been advised to remain there until it is safe to leave, but Britons able to leave Nepal safely have been encouraged to do so.
The Department for International Development (DfID) has already deployed a team of more than 60 search and rescue responders and medical experts to support the relief effort in Nepal.
A plane from London has been sent to Kathmandu, carrying seven search and rescue crews, four search and rescue dogs, a medical support team and a hazardous materials specialist.
The plane contained more than 11 tonnes of kit, including torches, axes, rope, search cameras, stretchers and tents.
A Foreign Office rapid deployment team to provide further consular assistance for British nationals was also on board, along with experts from leading aid agencies including the British Red Cross, Medecins Sans Frontieres and Map Action - an international disaster mapping charity.
Some 67 British firefighters from the International Search and Rescue Team (UKISAR) are also among those helping.
The team is trained to provide specialised technical search and rescue assistance in collapsed buildings.
Salisbury-based charity Serve On has sent eight volunteers from its international rescue team. They reportedly arrived in Nepal on Monday and have begun search efforts after liaising with UN co-ordinators.
An RAF plane carrying UK aid supplies and British army troops, including Gurkha engineers, has left for Nepal.