David Cameron says business deals worth more than £750m ($1.2bn) will be made during his tour of South East Asia.
Mr Cameron is to be accompanied by 31 UK business leaders on the trade mission, which starts in Indonesia.
The UK prime minister says he wants to forge links with the area’s rapidly growing markets for British goods and services during his four-day trip.
He will also discuss the threat of the self-styled Islamic State group and climate change during his trip.
Business Secretary Sajid Javid is leading a separate delegation to the region from the North of England.
By Ben Wright, BBC political correspondent
The prime minister’s crammed itinerary will take in Indonesia, Malaysia, Vietnam and Singapore on a whistle-stop trade mission, the first of this Parliament.
While the EU remains Britain’s biggest trading partner, Mr Cameron has been clear the UK needs to look beyond Europe, an ambition mirrored by frustration at the EU’s level of competitiveness and regulation.
Last week, he said Britain needed to go “to the ends of the earth” to sell its wares.
The prime minster is sending a clear signal Britain must look east.
Not just to India and China, but to the largely untapped potential of South East Asia as well. By 2030, the region is expected to be the fourth-largest single market in the world.
The prime minister said: “Over the next 20 years, 90% of global growth is expected to come from outside Europe, and Britain must be poised to take advantage.
“That’s why I’m delighted to be taking British businesses to this vast and dynamic market, securing deals worth over £750m and creating opportunities for hard-working people back at home.
“We can also open up more markets for British businesses by leveraging the power of the EU’s single market with 500 million consumers to secure bold, ambitious trade deals with these fastest, growing economies.”
During the trip, the prime minister is expected to push for progress on a free trade deal between the European Union and South East Asian trading bloc, Asean, which Downing Street believes could provide £3bn a year to the British economy.
Mr Cameron said he would be making the case for an EU-Asean deal in talks with the group’s secretary general Le Luong Minh.
Business leaders accompanying Mr Cameron include:
- Philip Bouverat, from JCB
- John Nelson, from Lloyd’s of London
- Ann Cormack, from Rolls-Royce
- Leo Quinn, from Balfour Beatty
- Mark Wilson, from Aviva
- Paul Kahn, from Airbus Group UK
- Vivienne Stern, from UK Higher Education International Unit
- Sir Martin Sweeting, from Surrey Satellite Technology
It will be the first time a British prime minister has visited Vietnam and the headquarters of the Association of Southeast Asian Nations (Asean), which promotes economic and trade growth among its 10 member states, in Jakarta, Indonesia.
Conservative MP Richard Graham has been appointed as a trade envoy specifically for the Asean economic community, which is due to be established by the end of the year, alongside the similar role he plays in Indonesia.
The UK government will also make up to £1bn available to finance infrastructure projects in Indonesia through its export guarantee scheme during the trip.
It hopes the financing could pave the way for growth of £200m worth of exports to the UK.
But the BBC’s Ben Wright said there could be diplomatic tension when the prime minister visits Indonesia if he raises the case of Lindsay Sandiford, who has been on death row in the country since 2013 for smuggling cocaine with a street value of £1.6m.
Mr Cameron will also urge closer counter-terrorism co-operation with South East Asian nations amid concerns IS will seek to gain a foothold in the region.
The threat of extremists will also be raised by Mr Cameron in meetings with President Joko Widodo in Jakarta and, later, Prime Minister Najib Razak of Malaysia.
IS and other militant groups have been using propaganda in local languages and their support is thought to be growing.