Business deals worth more than £750 million will be sealed during David Cameron's four-day tour of south-east Asia which begins in Indonesia today.
The Prime Minister, who will be accompanied by a group of business leaders from across the UK on the trade mission, wants to boost economic links with a part of the world Downing Street believes has "untapped potential" for Britain.
Mr Cameron will also focus on the growing international threat posed by Islamic State (IS) during talks in Indonesia and Malaysia.
He will also seek to build momentum for action to tackle climate change ahead of the United Nations summit in Paris at the end of the year.
On his first trade mission since being returned to Number 10 in May, Mr Cameron will become the first British prime minister to visit Vietnam.
He will also be the first prime minister to visit the headquarters of the south east Asian trade bloc Asean in Indonesia's capital Jakarta.
The trip, which will also take in a stop in Singapore, is aimed at increasing exports and forging trading links with rapidly-growing potential markets for British goods and services.
As part of the trade mission, the UK Government will make available up to £1 billion to finance infrastructure projects in Indonesia through its export guarantee scheme.
This financing could pave the way for growth of £200 million worth of exports to the UK.
Projects up for grabs include a sewage treatment system in Jakarta worth £400 million and geothermal power projects worth £66 million.
The Prime Minister will also push for progress on a free trade deal between the European Union (EU) and Asean which Downing Street believes could provide a £3 billion-a-year boost to the British economy.
Mr Cameron wants to strengthen ties with the developing economies as a way of reducing the UK's dependence on European trade.
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 £750 million 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.
"The EU has shown this can be done with the trade agreement with Singapore and the recent breakthrough in talks with Vietnam, but an EU-Asean trade deal would really turbocharge growth across the single market."
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.
"Alongside an EU-US trade agreement, such deals would be like a shot in the arm for Europe's economy," Mr Cameron said.
Tory 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.
Mr Cameron will also urge closer counter-terrorism co-operation with south east Asian nations amid concerns IS will try to gain a foothold in the region.
He will also use meetings with President Joko Widodo in Jakarta and, later, Prime Minister Najib Razak of Malaysia to raise the threat from the extremists.
IS - also known as Isil and Daesh - and other terror groups have been pumping out propaganda in local languages and their support is thought to be growing.
About 500 people from Indonesia - which has the world's largest Muslim population - and 200 from Malaysia are thought to have joined IS in Iraq and Syria.
There are also fears about the release of Islamist terrorists locked up in Indonesia following the Bali bombing in 2005.
In a sign of the growing appeal of IS in the region, Indonesian extremist leader Abu Bakar Bashir has pledged allegiance to the group.