In Cabinet meetings, when Britain’s International Trade Secretary Liam Fox trumpets the benefits of trade deals with non-EU countries after Brexit, the Chancellor Philip Hammond has a habit of telling him: “I look forward to you explaining the benefits of more New Zealand lamb imports to Welsh hill farmers.”

There, in a nutshell, lies the UK’s dilemma as the reality of Brexit starts to sink in. Next week we will hear a lot of talk about boosting trade with the Commonwealth when the biennial summit of its 53 leaders takes place in London and Windsor. Australia and New Zealand will be first in the queue. But the big prize – India—will take much longer.

On the face of it, the UK’s historic ties with the Commonwealth should put some flesh on the very bare bones of the Government’s “Global Britain” strategy – so far a vacuous slogan. The Commonwealth is home to 2.4 billion people, almost a third of the planet’s population, and one in three of its 15-19 year-olds; it represents about a sixth of global GDP and has half the world’s top 20 emerging cities.

Leave campaigners talked up Commonwealth links in the 2016 referendum. At the same time as playing on people’s anxieties about immigration, they dangled the prospect of more people coming to the UK after Brexit – such as curry house chefs and waiters from India.

With the EU’s share of global growth declining (largely due to China’s rise), Brexiteers argue that the Commonwealth offers a rosier future, and some saying it could eventually supplant the EU in UK trade relations.

“Nonsense,” according to Sir Lockwood Smith, New Zealand’s High Commissioner in the UK until last year. The EU accounts for 44 per cent of UK exports, and the Commonwealth about 9 per cent. Most economists cite geography as crucial factor in trade.

In return for trade deals, countries like India will want to export one thing in particular to the UK – people. There’s the problem. In Cabinet discussions, Brexiteers argue for a “level playing field” on migration between the EU and rest of the world.

But there is a growing recognition among ministers that they will have to give the EU migrants preferential access in order to secure a good trade deal. With employers demanding continued EU migration and Theresa May wedded to her nonsensical target to bring net migration below 100,000 a year, it doesn’t add up.

The UK may find that the national economic interest lies closer to home and the best possible EU trade agreement, rather than harking back to the days of empire when red dominated the world map.

May will talk trade with Commonwealth leaders next week and boosting it will be a key theme during the UK’s two years chairing the organisation. But hopes that the Commonwealth will become an “economic powerhouse” may not come to fruition.

It is not a supra-national body like the EU, and works by consensus. Some of its economies are very small. Some have little in common with the UK on human rights; homosexuality is criminalised in 36 Commonwealth states and the death penalty exists in 20.

Despite the Government’s rhetoric, MPs suspect it does not really prioritise the Commonwealth, but wants to pick the low hanging fruit of Australia and New Zealand to show it can land trade deals. Although the Foreign and Commonwealth Office (FCO) is deploying 250 staff overseas and opening 10 new posts to enhance “Global Britain”, the priority will be America, the Asia-Pacific region and – wait for it – Europe.

The FCO is not really living up to its full name, according to the Commons Foreign Affairs Select Committee. Tom Tugendhat, its Tory chairman, criticised the Foreign Secretary Boris Johnson’s attitude towards the Commonwealth. He told the liberal conservative think tank Bright Blue: “If the Commonwealth is not one of the priorities in a post-Brexit era, one wonders what is.”

We could hardly blame Commonwealth leaders for being wary of the UK’s overtures. Britain turned away from them when it joined the EU in 1973 and now wants to be best friends again. It has sometimes been patronising towards the Anglosphere. The Tories opposed sanctions against South Africa over apartheid.

Embarrassingly for May, a new scandal has emerged on the eve of the summit as a result of the tough approach to illegal immigration she ordered as Home Secretary. Seventy years after the first wave of (invited) Commonwealth migrants arrived on HMS Windrush, some of their children, having lived in Britain all their lives, are in danger of losing their job, benefits and free health care or even being deported because they were never given official papers or did not apply for a passport. An estimated 50,000 Commonwealth-born people who arrived before 1971 might not have regularised their status.

What better way for May to mark the Commonwealth summit – and the 50th anniversary of Enoch Powell’s “rivers of blood” speech – than to end such abhorrent treatment and declare that the people affected are still welcome?

The Independent.