Earlier this week, Alexander Downer, the former foreign minister of Australia and now the country’s High Commissioner to Britain, gave a wide-ranging speech at Oxford University’s China Centre. The contents were typically genial but frank. “During the time that I’ve been based here in London,” he observed, “I’ve been surprised how little attention Asia gets in this part of the world.”

Downer recently told BBC radio that the price of a free-trade deal for Britain in Canberra might be a more liberal visa regime for Australians. “We would want to see greater access for Australian businesspeople working in the UK,” Downer noted. “That’s often been a part of free-trade negotiations.”

In the post-Brexit world, Downer may well get his wish. Brexit is causing internal turmoil in British politics. But the moment when the country needs to seriously rethink its relationship with the world is fast approaching, as Britain seeks to exit the EU by spring 2019. The British government has made it clear it is seeking what is known as a “hard Brexit”: no attempts to remain a member of the single European market of 500 million people, and no attempts to remain part of the EU customs union.

In fact, this decision means Britain will actually need to do more, not less, about engaging with its European neighbours.

What appears to be lacking is gracious language about the peace and security that the EU has brought the continent since the second world war, if only to smooth currently fraught relationships between London and the continent. Most of the language about Europe in Britain today looks grudging and insular.

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Yet the really big task will be to bring the Indo-Pacific region to the forefront of British political and economic thinking. Top politicians from the prime minister and foreign secretary down have spoken of making Britain truly “global”. But so far, there have been few signs of a big-picture view of the world. There are occasional mentions of Australia as an old ally. But only 1 per cent of Britain’s trade is with Australia. Canberra’s biggest trading relationship is with Beijing, while its most important security relationship is with Washington.

Meanwhile, redefining Britain’s relationship with China and Japan, the second and third biggest economies in the world, remains an exercise with the phrase “fill in later” scribbled at the bottom. Huge rising powers like Indonesia are almost entirely absent from any public conversation in Britain. After 2019, the British government has made clear, Asia’s great economies can no longer use Britain as a gateway to the European market. So now is the time for London to provide an integrated picture on how its diplomacy, economics, and security concerns will come together.

First, there has to be a realistic grasp of what a global immigration policy means. Britain will regain control of its visa regime, but the areas where it excels – services such as finance, higher education, and entertainment (music and television) and high value-added manufacturing areas such as aerospace, nano/biotech, and pharmaceuticals will need a highly mobile internationalised working environment that means more, not less, traffic to Britain and yes, more immigration too.

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Major British institutions do big medical field trials in China. They are unlikely to be able to develop them further if Chinese scientists can’t come to Britain – and not just top laboratory heads, but the graduate students and postdoctoral fellows who are the lifeblood of global science.

Brexit may not directly affect Indians, whether business investors or software engineers, but it’s certainly sent a message that outsiders are unwelcome. That message needs to be reversed, and urgently.

Then, Britain will have to work out how to define itself as part of a changing Asian security environment. The Trump presidency may not have torn up all the rules in Asia, but it’s certainly made actors in the region such as Japan aware that they may well have to show more autonomous leadership.

Britain wants to trade with China and Japan. But if tensions between them rose over the next decade, where would Britain stand? Without the cover of the patchy but useful diplomacy of the European External Action Service (the EU’s foreign ministry), would Britain need to make a starker choice between sticking to its traditional security partners in Asia, or going with China, the biggest economic actor in the region?

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Britain’s government has taken a gamble with its electorate, since the “hard Brexit” decision endorses the decision of just over half the population who decided to leave the EU (52 per cent), while making no concessions to the nearly half of voters who wished to stay. A serious engagement with Asia will be essential if the plan is to succeed. In the next few years, Alexander Downer may yet see Britain spending a lot more time talking about China, Japan, India and Australia.