Theresa May has announced new visa and passport arrangements to make it easier for wealthy businessmen from India to come to the UK.
A small number of "high net worth" individuals and their families will gain access to the Great Club scheme to smooth the path of visa applications, while thousands of executives will be able to take advantage of the Registered Traveller Scheme to speed their passage through UK airports.
But the Prime Minister signalled she will resist pressure from New Delhi to ease restrictions for other student and work visas, insisting the UK already has a "good system" for applications from India.
Mrs May has travelled to India at the head of a 33-strong UK business delegation, with the aim of bringing down existing barriers to commercial links as well as paving the way for a free trade deal after Britain leaves the EU.
But her Indian counterpart Narendra Modi is expected to use talks in capital New Delhi on Monday to pile on pressure for relaxation of visa rules.
Indian Government spokesman Vikas Swarup said: "In the last five years or so, the number of Indian students enrolling in UK universities has gone down by almost 50% - from around 40,000 to about 20,000 now. This has happened because of restrictions on post-study stay in the UK.
"We will continue to raise our concerns regarding mobility with the UK. Mobility of people is closely linked to free flow of finance, goods and services."
Indian tech sector body Nasscom has also raised concerns about higher salary thresholds for skilled workers seeking UK visas, announced by the Home Office just days before Mrs May's arrival.
The organisation called for a high-skilled worker mobility agreement, warning: "A system that restricts the UK's ability to access talent is also likely to restrict the growth and productivity of the UK economy."
And former business secretary Sir Vince Cable said that Mrs May's opposition to relaxation of immigration rules had "screwed up" his efforts to forge a trade deal during the coalition.
Questioned over whether she is ready to consider further liberalisation as she arrived in India, Mrs May told reporters: "Look at the visa system we have at the moment. We have a visa system for countries outside the European Union which ensures that the brightest and the best are able to come to the United Kingdom.
"The figures show that we issue more work visas to India than (to) the US, Australia and China put together. Nine out of 10 visa applications from India are already accepted.
"So we have, I believe, a good system."
Under the Great Club scheme, a select few Indians and their immediate family members will be given personal account managers to smooth the process of securing visas.
The service, launched in 2013, is already used by around 100 of the non-EU world's most successful, but India will become the first country whose Government may nominate members.
As many as 10,000 more business visitors on work visas are expected to benefit from the Registered Travellers Scheme, which removes the requirement for landing cards on arrival in the UK and allows them to use e-passport gates to leave the airport quickly.
The scheme is so far restricted to just nine key non-EU trading partners - such as the US, Japan and Australia - and India is the first country to join whose citizens require visas to visit Britain.
Mrs May said: "As we leave the EU, we want to ensure that the UK remains one of the most attractive countries in the world to do business and invest.
"Over 800 Indian businesses are already invested in Britain, making India the second-largest creator of jobs here and the third largest inward investor.
"We want to attract more Indian businesses to the UK, which is why it's right to offer Indian business executives a world-class visa service tailored to their needs.
"The UK and India are natural partners and I want to achieve more together, recognising the untapped potential of this relationship and building a partnership that works for our shared security and shared prosperity."
Downing Street estimates the number of new jobs created by Indian investment in the UK in 2015/16 at 7,105, and officials said a further 1,370 are expected to be created by commercial deals due to be sealed during the PM's three-day trip.
Ahead of her meeting with Mr Modi, Mrs May was due to meet Indian business leaders at a tech sector summit in Delhi on Monday.