Image copyright AFP/Getty Image caption International Trade Secretary Liam Fox is accompanying Theresa May on the three-day trip

Theresa May has rejected calls to relax Indian visa rules, saying the UK has a "good system" for applications.

The prime minister, who is in Delhi to pave the way for the UK's first post-Brexit trade deal, said the UK was already able to attract "the brightest and the best" from outside the EU.

"Nine out of 10 visa applications from India are already accepted," she said.

But she said the UK could give ground if Indians who overstayed their visas could be returned more swiftly.

"The UK will consider further improvements to our visa offer if, at the same time, we can step up the speed and volume of returns of Indians with no right to remain," she told reporters.

Her government also intends to make it easier for wealthy Indian business executives to come to the UK.

A small group of high-net-worth individuals and their families will be offered access to the Great Club - a bespoke visa and immigration service - to make visa applications smoother.

Thousands of Indians on work visas will also be able to join the Registered Travellers Scheme which will mean they can get through UK border controls more quickly.

"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," Mrs May said.

Image copyright Reuters

Analysis: Simon Jack, BBC business editor in Delhi

The prime minister flew into Delhi late last night to be greeted by the worst smog this city has seen in nearly 20 years.

Where better to get a taste of life beyond the EU - than India. With such deep historical links between the two countries - surely the UK can cut through the bureaucratic smog that saw Brussels spend nearly a decade negotiating, but ultimately fail to agree a deal with the world's fastest growing economy.

But Indian business leaders are confused. No-one knows what the UK's relationship with Europe will eventually look like, and many are unsure about how much can be usefully discussed until the UK has withdrawn from the EU - a point that is at least two years away.

Some things are clear and all too familiar. Trade and immigration are linked. If the UK wants better access to Indian markets, the government in Delhi wants a looser approach to UK work and student visas. This week saw Britain's visa rules for foreign visitors tightened.

Specific deals will be announced over the next 24 hours but more clarity around a trade relationship that has stagnated or even declined in recent years is likely to remain enveloped in the Delhi smog.

Media playback is unsupported on your device Media caption Can UK boost trade with India post-Brexit?

Visa issues risk dominating Theresa May's first trade trip since becoming prime minister.

India's Prime Minister Narendra Modi told a technology summit in Delhi he wanted to encourage "greater mobility" for its young people in education.

He said: "Education is vital for our students and will define our engagement in a shared future.

Media playback is unsupported on your device Media caption Ex Independent border control spokesman tells The World at One that there has been a rise in Indians returning voluntarily

"We must therefore encourage greater mobility and participation of young people in education and research opportunities."

Cobra Beer founder Lord Bilimoria earlier said restrictions on staying in the UK after their studies meant the number of Indians attending UK universities had halved in the past five years.

He said "movement of people" would form a key part of any trade negotiations.

'Bridge-building'

The number of study visas issued to Indian nationals fell from 68,238 in the year to June 2010 to 11,864 five years later, official UK figures show.

The solution, according to Karan Bilimoria, is to exclude foreign students from Britain's statistics on net migration, which Mrs May has pledged to cut to below 100,000 annually - down from 336,000 in the year to June 2015.

"We need to immediately get the government, Theresa May, on this visit to announce and say 'we're no longer going to include international students within the net migration figures,'" crossbencher Lord Bilimoria told BBC Radio 4's The World This Weekend.

He added: "The reality is Theresa May when she was home secretary did deliver very, very negative messages towards immigration."

"She has got a lot of bridge-building to do when she goes to India."

Mrs May will be accompanied on the three-day trip by International Trade Secretary Liam Fox and trade minister Greg Hands as well as representatives from 33 UK companies.

Deals expected to be confirmed during the trip include: