Madeleine Sumption, director of the Migration Observatory, adds she “would be surprised” if a trade deal with India had a transformative impact on the UK immigration system and by extension, the labour market.

She says: “The types of measures that you see in trade agreements tend to be tinkering around the margins rather than fundamentally changing the immigration system for a particular country. You’re often looking at a slightly easier administrative process, maybe a slightly lower cost, maybe they can be in the country for slightly longer.”

Despite senior British Asian figures around the cabinet table such as Chancellor Rishi Sunak and Home Secretary Priti Patel, politics is also likely to intervene. With Channel boat crossings a touchstone issue for the “red wall”, ministers do not want to be perceived as a soft touch; May’s agreement also put as much emphasis on the return of illegal Indian immigrants as movement of labour.

Migration Observatory’s Sumption adds: “There are often tensions within governments between immigration policymakers and trade policymakers, because the trade policymakers have an incentive to put immigration on the table. For immigration policymakers, doing that is a bit of a pain because it makes the system they’re trying to manage more complicated.” 

While Lord Bilimoria stresses that “no one is asking for open borders”, he says: “Mobility has historically been important and will continue to be important in both countries’ interests – and both ways”. 

Even if higher Indian immigration is unlikely to solve Britain’s labour market woes, the outcome of the talks could be a totemic moment. Johnson wants to project an outward looking Global Britain but faces Sir Edward’s calls to “connect to our supporters and control immigration”. 

Squaring the circle will test the PM’s political skills to the max.

Let more Indian workers into Britain, says CBI’s Bilimoria

Lord Bilimoria, the CBI president, has pressed for looser visa restrictions between India and the UK ahead of the formal launch of trade talks between the two countries this week.

The intervention of the Cobra beer founder, one of the UK’s most prominent British-Indian businessmen, comes as the International Trade Secretary, Anne-Marie Trevelyan, prepares to fly to Delhi in pursuit of a deal.

The peer said that “no one is asking for open borders” but added: “Mobility has historically been important and will continue to be important in both countries’ interests – and both ways.”