IN THE 1950s nearly half of India’s imports and 80% of its foreign investment came from Britain. Today Britain ranks 13th among India’s trading partners, accounting for 2% of its trade. British firms still have big investments in India, but now such brands as Jaguar Land Rover, Tetley’s tea and even the East India Company are Indian-owned. And it is now Delhi, India’s capital, that cooks up the thickest and smokiest of those fogs that London once made.

So Theresa May discovered as she arrived on November 6th, into a haze unusually acrid even for the world’s most polluted big city. The prime minister’s three-day visit, her first outside Europe, was meant to show that a post-Brexit Britain can prosper by reviving old friendships and cutting new deals. But even Delhi’s smog could not obscure some hard truths.

Mrs May had hoped to focus on trade and investment. The Indian ministers and businesspeople she met with, however, were fully aware that Britain will be in no position to negotiate significant bilateral deals until it has sorted out its disentanglement from the European Union.

India’s government, meanwhile, has shown scant interest in trade deals. Talks on a free-trade agreement with the EU that began in 2007 have been stalled since 2013. India last year shied away from joining the Trans-Pacific Partnership (which now itself looks doomed). And earlier this year Delhi told 57 countries that it wishes to scrap and renegotiate its bilateral investment-protection treaties with them. Its new “model” treaty would compel foreign investors to seek redress in India’s clogged courts before doing it via international arbitration.

Rather than freer trade with Britain, what Indian officials pressed for was greater freedom of movement. Small wonder. During Mrs May’s six-year tenure as home secretary, the number of Indian students in British universities plummeted from 68,000 to 12,000, largely due to her tightening of visa rules. To Mrs May’s discomfort those rules tightened further a few days before her visit. Foreign companies will now find it harder to bring over staff for short-term postings in their British subsidiaries; Indian tech firms had accounted for 90% of migrants in one of the affected categories.

“It seems that the UK is mainly interested in greater market access for its goods in India and in getting investments from India, but not in attracting talented Indian services professionals and students,” sniffed Nirmala Sitharaman, a minister with portfolios in trade and finance. Narendra Modi, India’s prime minister, was just as blunt. Education, he declared at a public meeting with Mrs May, would “define our engagement in a shared future.”

Given Mrs May’s promise to curtail immigration even further, the British team could not offer much on this score. She did pledge shorter queues for Indian frequent flyers to Britain. They can now hope to join the “Great Club”, an invitation-only portal which, Mrs May said, will provide lucky executives and their families “a world-class visa service tailored to their needs”. Any further easing of visa rules, she warned, would hinge on India’s willingness to take in more of the people that Britain wants to expel from its shores.

This prompted one Indian wit to tweet: “This is funny. Theresa May wants India to ‘take back’ Indians who overstayed but won’t extradite Vijay Mallya who has no passport.” The reference was to a prominent Indian businessman who took refuge in London earlier this year as Indian creditors demanded repayment of more than $1bn. Britain says India has yet to present extraditable charges against Mr Mallya.

The air cleared as Mrs May headed to Bangalore, India’s tech capital, for visits to a factory and to a Hindu temple, clad in diaphanous Indian national dress. “She carried her sari remarkably well,” says one fashion critic in Delhi. Yet the promises of future co-operation were just as thin.