Theresa May will tell the leaders of the world’s most powerful economies that the United Kingdom wants to strengthen its economic ties with countries beyond the European Union, as she lays out her vision of a post-Brexit Britain at her first big international summit as prime minister.

Attending the G20 meeting in Hangzhou, China, May will address the opening session saying that, as the UK heads out of the EU, it remains “open for business” and is seeking to build new and stronger trade relations with countries across the globe.

But diplomats past and present warned that she faces a huge test as a novice on the world stage, and will have to perform a delicate balancing act as she seeks to sell the UK to global leaders, while avoiding giving the impression that Britain is about to become a marginal player on the European stage.

In a sign of her determination to show that the UK is embarking on a new phase in its diplomatic and economic relations, May will hold four bilateral meetings with the leaders of the US, China, Russia and India, but none with EU leaders.

British officials have denied that she is cold-shouldering the Europeans, and stressed that since becoming prime minister she has already met the leaders of France and Germany to address the challenges of Brexit. The G20, they said, is her chance to convince other world leaders that the UK is a “dependable” partner which will “continue to play a bold confident and outward-looking role as it leaves the EU”.

Speaking on BBC1’s The Andrew Marr Show on Sunday morning, recorded before she left for the G20, May said the economic figures were not as bad as some had predicted after the EU referendum vote. “What is important for us now is that we maintain that policy of ensuring economic stability and a strong economy for the future. Part of that is going to be, as we come out of the European Union, ensuring we’ve got trade deals around the world. I want the United Kingdom to be a global leader in free trade.

“One of the things I’ll be doing at the G20 is emphasising the role that we will be playing in the world, but also in a number of the discussions I’ll be having, with President Obama, for example, prime minister Modi, prime minister Turnbull … ”

A bilateral meeting with President Xi Jinping of China, after the official summit proceedings close on Monday, will arguably be May’s sternest test. Her decision, shortly after entering Downing Street, to delay a go-ahead for the Hinkley Point C nuclear plant in Somerset, on which China has committed to spend billions of pounds, has severely strained relations with Bejing.

The former UK foreign secretary Sir Malcolm Rifkind told the Observer that the G20’s Chinese hosts would be “surprised and puzzled” by the UK’s vote to leave the EU, but would probably be more attentive to May as a result. “Although they will think that we are slightly barking for wanting to leave the EU, they will in some way see us as more interesting and needing more of their attention. We will be the second biggest economy in Europe, a permanent member of the UN security council, and a strong military power with the willingness to use that power.”

However, Rifkind said the Hinkley Point issue would hover over the summit. “Whatever the wider and longer-term issues, Hinkley is the immediate test. The Chinese president and UK prime minister will be sizing each other up. Hinkley Point is directly relevant to China’s global economic ambitions.

“If we drop Hinkley Point, and even if we stress that this is for economic reasons alone, the Chinese will see it as a major defeat for their ambitions. We will be seen as joining with the US and Australia in rejecting China as a partner, and that will not be helpful for relations. This may be the right decision for the UK to take, but there will be a price to pay.”

May told Marr: “I’m looking at the Hinkley decision, but it’s about how I actually approach these things. I look at the evidence, I take the advice, I listen to that. That’s what I’m still doing. I’ve said there’ll be a decision in September.”

Lord Wood of Anfield, a former senior adviser to Gordon Brown, said May would be thrown in at the deep end of international diplomacy at a crucial moment in the UK’s history. There was a risk of being seen as a bit player in Europe.

“Theresa May has a tricky combination of challenges this week. In the wake of Brexit, she has to show that Britain’s relationship with Germany, France and Italy is not suffering,” Wood said. “She has to show that European ‘caucusing’ prior to and during the G20 is still alive and well. Any hint of Franco-German-Italian cosiness that excludes her risks suggesting we are on the way to becoming a second-tier G20 country. She will also need to consider the appropriate mixture of robustness and conciliation to adopt in her dealings with Vladimir Putin.”

On her meeting with Barack Obama, Wood added: “She will have to show that Britain still matters to an outgoing president who has been increasingly speaking his mind, and whose advice on Brexit was conspicuously rejected by the British electorate.”

Before boarding her plane for China, May insisted that UK-China relations have a bright future. “This is a golden era for UK-China relations, and one of the things I’ll be doing at the G20 is obviously talking to President Xi about how we can develop the strategic partnership that we have between the UK and China. But I’ll also be talking to other world leaders about how we can develop free trade around the globe and how Britain wants to seize those opportunities.”

Global security and the fight against terrorism will also be high on the prime minister’s agenda.

Margaret Thatcher’s former foreign policy adviser Lord Powell of Bayswater said he expected May to approach the G20 in a much more cautious manner than his former boss, who would have piled in with her demands and views. May would be more concerned with “signals” than substance.

“In one day to be seeing Obama, Putin, and Xi Jinping is quite a scorecard. She will want to show that she believes the UK can make a success of Brexit. It will be a case of signals more than getting down to any definitive business.”

ENEMIES ABROAD?



Xi Jinping



Xi Jinping. Photograph: Reuters

China’s president said on a state visit to London last year that he hoped Britain would be a “gateway to Europe” for his country. George Osborne, the then chancellor, talked of the UK being China’s “best partner in the west” and of a golden era of British-Chinese relations. Now, with Britain heading out of the EU and doubts over whether Theresa May will go ahead with the Hinkley Point C nuclear power project, into which China has agreed to pump billions of pounds, relations are tense. China has already made clear that it would regard abandonment of the project as a snub. After the summit, May will have a bilateral meeting with Xi at which she will make clear that the decision will be for the British government alone. Xi will view the eventual decision by the prime minister later this month as a test of how dependable the UK is and of its wider willingness to be a partner in China’s developing global economic ambitions.

Vladimir Putin



Vladimir Putin. Photograph: EPA

May will have a bilateral meeting with Putin on Sunday at which difficult security issues, including Russia’s role in Syria and actions in Ukraine will be raised. The Russian president is almost certainly the only G20 leader who will have welcomed and seen overall benefits for his country from Britain’s intended departure from the EU. Russia sees it as a sign that the bloc on his doorstep is no longer such a cohesive force and threat to his interests. Putin will also see potential for closer economic ties with the UK and may be looking for indications that the EU’s resolve behind sanctions against Russia will now weaken. But May will not want to risk angering the US or her EU counterparts, with whom she must negotiate Brexit, by cuddling up too much to Moscow.

François Hollande



François Hollande. Photograph: EPA

With Hollande facing presidential elections next year, he is sending a tough message to the British prime minister about future relations with Europe. France is adamant that the UK cannot expect special favours from the European Union - in terms of an exit deal - that undermines the founding principles of the EU. Hollande fears that this would merely encourage backing for anti-EU campaigner Marine Le Pen and the Front National, who will say that the French would also be better off out of the EU. France’s Socialist president’s message will be that there is a stiff price to pay for Brexit. Concerns over immigration and the future role of UK border guards in Calais may also be discussed.

RELATIONSHIPS TO WORK ON



Angela Merkel



Angela Merkel. Photograph: AFP/Getty Images

Theresa May has already been to Berlin for a meeting with Merkel since becoming prime minister and relations between Europe’s two most powerful women were reasonably warm. No bilateral has been planned for the G20, however, signalling the UK’s wider ambitions post-Brexit. As the EU’s power broker, the German chancellor, who like Hollande is facing elections next year, has a balance to strike between remaining close to the UK while preserving the EU intact. Germany fears that the UK will try to bolster its economy post-Brexit by trying to lure in foreign investment through low corporate and other taxes. Berlin wants to make clear that if this is the route it chooses then its access to the EU single market, particularly for the sale of financial services, which represent more than 10% of the UK economy, will not be possible.

King Salman



King Salman. Photograph: AFP/Getty Images

Saudi Arabia has spent £3bn on arms from the UK since the start of 2015, with critics voicing concerns that weapons may have been used against civilian targets in Yemen. The UK government would take a dim view if that were the case, but as it heads into a uncertain future outside the EU, May will not want to turn her back on what the UK government has identified as one of its priority markets abroad.

Narendra Modi



Narendra Modi. Photograph: EPA

Theresa May has a bilateral meeting arranged with the Indian prime minister on Sunday, another sign that the UK is looking increasingly outside Europe for economic ties and trade deals as it heads for Brexit. India is an obvious choice for trade talks, with its huge developing markets. Modi will have his own concerns, however, about UK plans to tighten border controls and curb immigration, and will want reassurance that there will be continued access for skilled workers and students from his country into the UK.

SPECIAL FRIENDS



Barack Obama



Barack Obama. Photograph: AP

May has a bilateral meeting with Obama early on Sunday. The American president will want to sound out the new British prime minister about Brexit and what it means for the “special relationship”. The US always valued the UK as a route through which to convey its views to Europe, and is fearful of Brexit. It is also concerned that with the UK outside, EU support for sanctions against Russia over Ukraine will weaken. Obama said before the Brexit vote that the UK would go “to the back of the queue” in trade talks if it left the bloc. With the impending likely collapse of the US-EU Transatlantic Trade and Investment Partnership, however, could there be more of an opportunity now for the UK to jump to the front of the list of countries seeking bespoke deals with Washington?

Justin Trudeau



Justin Trudeau. Photograph: Reuters

There has been much talk of the UK, after Brexit, striking a trade deal with the EU similar to the one Canada is finalising with Brussels after years of intensive and difficult negotiation. The Canadian prime minister and May will no doubt exchange notes on how possible and desirable a similar arrangement will be for the UK, and how they could work together on the shape of future world trade. One problem is that Canada’s deal does not cover financial services, which contributed £126.9bn in gross value added to the UK economy in 2014. So the Canada model is no panacea. It has also taken almost a decade to strike and has yet to come into force.

Malcolm Turnbull

Malcolm Turnbull. Photograph: AAP

Australia has already called for a free trade deal with Britain following its exit from the EU – a move that May described as “very encouraging”. She insisted it showed Brexit could work for Britain. The Australian prime minister said he urgently wanted to open up trading between the two countries as soon as possible, and the G20 meeting will be a good opportunity to reaffirm their joint interests. While trade with Australia will not replace access to the single market, it will be a sign of the British willingness to look far and wide as it seeks new trade arrangements across the globe.