Prime Minister David Cameron’s visit to India this week could be overshadowed by New Delhi’s concerns over plans to further restrict immigration from India and other non-European Union countries, a member of his delegation warned on Monday.

Jo Johnson, a Conservative MP and a former Delhi bureau chief of Financial Times, said there was deep resentment in New Delhi over the proposal to impose an annual cap on immigration, and ministers had expressed concern that it could have an “adverse” effect on relations between the two countries.

Accusing the Cameron administration of sending “contradictory messages” to India by making travel more difficult at a time when it was trying to woo Indian businesses and talking of “enhanced” partnership, Mr. Johnson contrasted this with American efforts to ease restrictions for Indian entrepreneurs.

“The U.S. is genuinely throwing open its doors to Indian entrepreneurs, creating a pool of entrepreneurial talent there which we certainly should envy. I think there is a contradictory message to a certain extent. We need to be competing for the Indian entrepreneurial classes. We must encourage them to come and invest here,” he told the BBC.

Mr. Johnson said America’s start-up visa programme was “deliberately targeting the Indian entrepreneurial classes, saying to them come-come and invest here”.

His remarks came as the Union Commerce and Industry Minister Anand Sharma was reported as saying that the proposed restrictions could “hurt” the growing economic engagement between the two countries.

Mr. Sharma, who raised the issue with Mr. Cameron during his recent visit to London, was quoted as telling a British newspaper: “These immigration policies would affect adversely the professionals, Indian doctors, engineers and nurses, who have made a notable contribution to the U.K. economy. It could have an adverse impact, that’s why I’ve raised it. I’ve asked the Prime Minister and Foreign Secretary to intervene so it won’t hurt the growing engagement.”

Unease over cap

Another member of Mr. Cameron’s delegation, the Universities Minister David Willetts, was also said to have voiced his unease over a rigid cap. Universities, which depend heavily on fee-paying foreign students for income, said it would have a debilitating effect on their already fragile financial health. Leading British businesses are also opposed to an artificial limit.

The criticism dented some of the breathless hype over Mr. Cameron’s visit, billed as the most important trip by a British Prime Minister to India in a generation. He has told the heavy-weight business delegation accompanying him to send out a message that Britain was “open for business”.

A £500-million arms deal to sell 60 Hawk jets to India is among a string of agreements expected to be signed during the three-day visit aimed at exploring business opportunities in India’s growing market.

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