By Jenny Gross

NEW DELHI--British Prime Minister Theresa May on Monday said the U.K. may make improvements to its visa system for Indians, as she sought to lay the foundations for a future trade deal once Britain leaves the European Union.

On a two-day trip to India focused on trade, Mrs. May, speaking alongside Indian Prime Minister Narendra Modi, said the partnership between the U.K. and India was natural, since the countries have shared values and culture. But a key sticking point in U.K.-India relations has been Britain's reluctance to loosen restrictions for Indians wanting to work or study in the U.K., and this will likely be a difficult point to settle in any free-trade negotiations.

"The U.K. 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 in the U.K.," she said.

Mrs. May is unlikely to implement any changes that would result in big increases of Indians entering the U.K. She has said the June vote to leave the EU was underpinned by frustrations about rising levels of immigration and has pledged to reduce numbers.

The U.K. is seeking to go beyond its traditional trading partners in Europe as it prepares to leave the European Union. While it can't finalize trade deals while still a member of the EU, Britain is in preliminary discussions on trade with countries including Australia and India, the world's fastest-growing major economy. Any deal is likely to take years to complete.

Mrs. May defended the U.K. visa system, saying it worked well and that the U.K. wanted to attract the best ofIndia while keeping migration down.

Earlier, Mr. Modi briefly raised the issue, saying education will define the engagement between India and the U.K. in the future.

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

Mrs. May, who announced several investments in Indian companies, said she wants Britain to be the most passionate advocate of free trade around the world, and that the U.K. and India need to make the case for continued free trade to increase stability and prosperity. Her comments come at a time when governments around the world have expressed doubts about the benefits of free trade.

Write to Jenny Gross at jenny.gross@wsj.com

(END) Dow Jones Newswires

November 07, 2016 06:40 ET (11:40 GMT)

Copyright (c) 2016 Dow Jones & Company, Inc.