India is expected to demand more immigration into the UK as part of any post-Brexit trade deal, posing a dilemma for Theresa May as the prime minister prepares to travel to the country for her first bilateral visit outside Europe.

Business leaders and government officials expect the vexed issue of Indian visas for the UK to be a central part of negotiations, with initial business-to-business discussions expected to open soon after Mrs May leaves.

Patricia Hewitt, chair of the UK India Business Council, said both countries would seek a “modern agreement” involving both goods and services. “And when you talk about services, some of that involves the temporary movement of people.”

Chandrajit Banerjee, head of the Confederation of Indian Industry, said: “It is very important for business that people have more access to work in Britain, and this will be a key demand in any trade talks.” One Indian government official added: “We want everything to be on the table, and that will have to include visas.”

Disagreements over visa restrictions have been a stumbling block in separate talks between India and the EU which have dragged on for nearly a decade: Delhi is said to have demanded 50,000 working visas a year from the bloc.

Any relaxation of the rules governing employment would be sensitive given that Mrs May is sticking to her pledge to reduce net migration below 100,000 per year.

The prime minister hopes to kick-start early talks on trade with her visit next week. Initially these are likely to be informal discussions involving businesses and civil servants, with formal negotiations not allowed to start until the UK has left the EU, likely to be in 2019 at the earliest.

The UK wants the liberalisation of service sectors including insurance, accountancy and legal services.

“India-UK trade has suffered in part because services are such a big part of what the UK exports, but strict Indian laws regarding what services can come from abroad have held them back,” said Ms Hewitt.

One former Tory minister said: “You see the Germans and Italians easily exporting their engineering to India but it’s harder for us given their restrictions on important services industries such as insurance.”

Mrs May’s predecessor David Cameron travelled to India three times in his six years as prime minister.

On entering office, he pledged to double trade with India within five years, but found it impossible to meet that promise.

In recent years, total bilateral trade has fallen from $15.7bn in 2011-2012 to $14bn in 2015-2016, despite India’s strong growth. The UK currently sits 13th in the list of India’s trading partners, according to figures from the Indian commerce department — behind Germany, Indonesia and Belgium.

One of the key planks of Vote Leave campaign’s argument during this year’s referendum was that it would enable Britain to sign bilateral agreements with fast-growing countries such as India.

Liam Fox, trade secretary — who is on the trip — recently said a new trade deal would give British business more access to India’s 1.3bn consumers and that a “trade working group” was already being set up. “There is nothing to stop us having discussions and scoping out future agreements,” he said.

But one Tory colleague warned there was no “quick win” to be had: “Stepping up trade to India is very hard … we have to compete with a lot of emerging countries who are nearer to India and have a lower cost of capital.”

Indian businesses are optimistic about the possibility of a bilateral agreement with the UK, saying it would be easier to negotiate than the proposed deal with the EU, which remains incomplete after nine years and 13 rounds of talks.

But ministers in New Delhi say they remain confused by the sort of relationship Britain wants with the rest of the EU, not least whether it wants to remain part of the customs union, which governs what tariffs it can impose on imports.

They also say that while the UK continues to clamp down on visas from India, the country is unlikely to give Britain’s service sector favourable treatment.

New Delhi has long complained about the visa policies implemented by Mrs May when she was in the home office, including a reduction in student visas that have seen numbers fall more than 50 per cent from 2009/10 to 2014/15.

One option also being considered in New Delhi is not to sign a free-trade agreement at all, but instead to work towards giving the UK a watered-down “most favoured nation” status. This would mean tariffs on British goods could not exceed those implemented on any other country.

Mrs May, who is speaking at a Tech Summit in Delhi, is travelling with various business figures including the billionaire entrepreneur James Dyson. She is expected to attend a round table including Cyrus Mistry, who was recently replaced as chairman of the Tata Group, the conglomerate that owns Tata Steel. Earlier this year the group threatened to quit the UK with the loss of thousands of jobs.

Mrs May may be hampered by a lack of profile in India. Ram Madhav, the national general secretary of the ruling BJP, wrote in the Indian Express this week: “A majority of us didn’t know a leader by the name of Theresa May existed.”