WHEN Britain eventually leaves the European Union it will prosper by trading farther afield. So argues Theresa May, Britain’s prime minister, ahead of her first big bilateral trip abroad, a three-day visit to India, which begins on Sunday, November 6th. She talks of forging a “new global role” with this trade mission, hobnobbing with Indian leaders and championing free trade in general. The idea is to promote ties between small and medium businesses in the two countries. Yet creating a stronger economic relationship with India will prove much tougher than Mrs May and her colleagues expect.

On the face of it, the signs are good. India has nearly 1.3bn people. Many are emerging as middle-class consumers for the first time. The country is creating a single market for goods and services, reducing internal and external barriers to trade and tackling some corruption and bureaucracy. Its economy, worth over $2trn, is the fastest-growing large one in the world. It is likely to rattle along quickly for many years to come; by 2030, India could rank as the world’s third-largest. The prime minister, Narendra Modi, wants to make it less difficult for businesses to operate there, and to win more foreign investment and trade deals. British firms are already among the biggest investors. Now India is opening up for foreign activity in sectors that might suit British firms especially: notably in insurance, defence, railways and some retail. At the same time, large Indian firms—such as Tata, which owns Jaguar Land Rover, as well as Tata Steel—are in Britain. London has also become a base for Indian firms, for example in business consulting, that tap the wider EU market. A common language, shared cultural, historic, legal and sporting ties, plus the influence of the Indian diaspora in Britain, bode well for closer ties.

Mrs May is thus right to reach out. But anyone expecting quick gains will be disappointed. One of India’s priorities, for example, is avoiding complications over a long-stalled free trade agreement with the EU, which has been under negotiation since June 2007. After 12 rounds of talks, some consensus has been found on issues including trade in rice, sugar, textiles and pharmaceuticals. It is not clear that India’s overstretched trade negotiators will see much benefit in being diverted to work on a deal with Britain alone, especially if that makes it harder to complete one with the bigger EU market. Even if they do decide to talk biltaterally, among the sticking points has been India’s 150% tariff on imports of whisky from Scotland. Future British negotiators would struggle to be more effective than their European counterparts at getting that scrapped. The biggest concern, however, is about Britain’s ever colder shoulder towards Indians who want to travel and study there. Under the Conservatives, Britain has in the past six years become less welcoming to foreigners, notably from South Asia, who hope to attend university and then work. Eye-wateringly expensive visas, increasingly hostile rules to get them, official talk of cracking down on foreign students in Britain, and graduates who lose the right to work after finishing a degree in Britain all leave Indians feeling unwelcome. Anecdotes abound of bright Indian students who win places at the best British universities but are refused visas to travel. Perceptions of generally rising xenophobia in Britain are discouraging to Indians too.

For Mrs May to win a warm welcome in India she needs to offer a message that is not only about investment and trade, but also sets out that Britain—in particular its universities—will again become more open to Indian visitors, migrants, students and their families. America is proving far more successful at attracting the highest-skilled migrants, especially software and other engineers. Other countries, including some in Europe, are rolling out policies to attract more Indian students to their universities. Yet Britain appears more hostile to migrants than it has in many decades. Within a few years, it is worth remembering, India’s economy will be bigger than Britain’s. Welcoming more exchanges of people, as well as encouraging higher levels of trade and investment, would make sense for both sides.