Theresa May has dashed Indian hopes for a more liberal visa system for its nationals wanting to work in the UK by arguing that the current offer is generous enough.

Speaking on the way to her first bilateral meeting in Delhi, the prime minister argued that Britain was already able to attract the “brightest and best” from outside the EU. “The figures show that we issue more work visas to India than I think US, Australia and China put together. Nine out of 10 visa applications from India are already accepted. We have, I believe, a good system,” she said.

The comments will prove disappointing for some in the Indian government and business community who have argued for more of their highly skilled professional workers to be able to get six-month visas for the UK and other European countries.

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The demand for more freedoms for Indian workers moving abroad was a part of trade negotiations with the EU, which stalled because of failure to agree on it and other issues.

Vince Cable, the former Lib Dem business secretary, said May’s refusal to agree to any such liberalisation in the past was a key stumbling block to trade talks between the EU and India. Although he admitted they were complex negotiations, he claimed that her unwillingness to budge was down to an obsession over getting the net migration numbers down as home secretary.

May said she hoped that her three-day visit to India would pave the way for a future trade arrangement after Brexit as she sought to break down barriers. However, she suggested she did not think a more generous visa system was necessary.

“Trade is an important part of our relationship with India. India is the third-biggest investor into the UK – second-biggest creator of private sector jobs in the UK. And the UK is the biggest G20 investor into India, but there is more we can do,” she said.

May was joined by a delegation of business representatives for a trip during which she attended the India-UK tech summit in Delhi with Prime Minister Narendra Modi before a bilateral meeting.

Modi used a speech to heavily hint that he wanted young people to be more able to travel abroad to study, after stricter rules in Britain on how long graduates can stay contributed to a halving of the number of Indian students coming to the UK to study over five years.

“Education is vital for our students and will define our engagement in a shared future. We must therefore encourage greater mobility and participation of young people in education and research opportunities,” he said.

May used her speech to the tech summit to insist she wanted an open relationship with India, laying out plans for India to become the first visa country to be put on a registered traveller scheme which helps speed up the experience of visitors in British airports.

“That means for Indian nationals who frequently come to the UK – and who fuel growth in both our countries – the entry process will become significantly easier. Fewer forms to fill out, access to EU/EEA passport control, swifter passage through our airports,” she said.

Despite the reluctance to increase migration numbers from India to the UK, the prime minister delivered a passionate argument for free trade between the two countries arguing that it “creates a rising tide that lifts all boats”.

She said Britain was determined not to turn its back on the world, adding: “Because we know from history what happens when countries do not embrace the opportunities of the world; they stagnate, they get poorer, they don’t protect their people, they make them worse off.”

Adding that while countries like India did not owe Britain a living, she said working together meant the greatest chance of success.

May also said she did not need to wait to leave the EU to start discussions on how trade and investment could be boosted between the countries.

However, she had earlier made clear she was aware of sentiment in the UK about immigration, and her promise to stick to an ambition of reducing the net migration figure to the tens of thousands would require cutting the numbers from all over the world.

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The response could disappoint those of Indian origin in the UK and those with links to other Commonwealth countries, after Brexit campaigners suggested they would benefit from an immigration system that no longer discriminated in favour of Europeans. Out campaigner and president of the Bangladesh Caterers Association, Pasha Khandaker, said he was “very disappointed” by the government saying it is ruling out an Australian-style points-based system as promised by Vote Leave during the referendum campaign.

May has attempted to deflect any row with an offer to make India the first visa country to be added to the Registered Traveller Scheme, under which business travellers can clear border control more quickly in British airports. It will allow passengers to come through the e-Passport gates, usually reserved for Britons and Europeans, and without a requirement to complete a landing card.

Only nine other countries currently benefit from the scheme, including the US, but they are not places where travellers need visas.

The government will also offer a group of high net-worth Indians access to a bespoke visa and immigration service called the Great Club. That doesn’t offer any guarantees but means individuals – and their immediate family members – are provided with a personal account manager to help them secure visas more quickly and smoothly.

However, the offer falls short of a pilot set up by the prime minister during a recent trip to China for a G20 meeting that cut the price of two-year tourist visas from £330 to £87.

Ahead of this trip, Chandrajit Banerjee, the director of the Confederation of Indian Industry, told the Financial Times that he was “very, very hopeful” that the prime minister would offer a similar liberalisation to Indian visitors.

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It followed a letter from senior executives including the heads of Heathrow airport and Virgin Atlantic calling on the government to cut the cost of tourist visas for India – saying that 400,000 Indians visited Britain last year spending £433m. However, they warned that France had become a more popular destination.

May is likely to address this issue during her talks but a source played down the issue, stressing that the Chinese price cut is a pilot scheme.

The registered travellers scheme will initially be offered to Indians travelling on a work visa, with the possibility of rolling it out to other routes in the future. The government estimates that up to 10,000 Indians could benefit from it within the first two years.