Manmohan Singh said he had conveyed his serious concern to David Cameron over the claims in regards to the helicopter deal. Photograph: Prakash Singh/AFP/Getty Images

David Cameron’s trip to India has run into trouble after his Indian counterpart raised “very serious concerns” a couple of £483m helicopter deal, and urged Britain to enhance its visa system.

An attempt by Cameron to recast Anglo-Indian relations as a “special partnership” was at risk of being overshadowed by the carefully worded intervention from Manmohan Singh.

Singh said at a joint press conference in Delhi that he had sought British assistance within the investigation into allegations that corrupt payments were made during negotiations to buy 12 AgustaWestland luxury AW101 helicopters, manufactured in Yeovil.

Giuseppe Orsi, the chairman and chief executive of AgustaWestland’s parent company, Finmeccanica, was arrested by Italian police as a part of an investigation into allegations that bribes were paid to Indian government officials. Orsi, who denies the allegations, resigned on Friday.

Singh said: “I conveyed to the prime minister our very serious concerns regarding allegations of unethical means used to secure the 2010 contract for AgustaWestland helicopters. I told him that we’ve got sought a proof from the corporate by 22 February to ascertain if the contractural conditions on unethical practices and the integrity pact were violated.

“i’ve got sought full the help of the united kingdom consequently. Prime minister David Cameron has assured me of co-operation of his government within the investigations.”

Cameron said Britain would co-operate, though he talked about that Finmeccanica was an Italian company. “We can reply to any request for info,” he said. “i’m glad that the Italian authorities are looking into this issue intimately as Finmeccanica is an Italian company, the parent company of AgustaWestland.

“Let me make absolutely clear that during Britain we’ve introduced anti-bribery legislation it really is probably the strongest anywhere on earth. We shall root out any problems of bribery or corruption wherever they seem and whenever they seem.”

Singh also showed Indian concerns over Britain’s tough visa system, which was heavily criticised by British and Indian business leaders for acting as a barrier to links between the countries.

The Indian prime minister said: “Education and science are special areas of India-UK co-operation. i’ve impressed upon the prime minister the necessity for a visa regime that facilitates greater movement of individuals between our two countries so this co-operation can be further recharged.”

Cameron said Britain had taken steps to sit back visa rules, and that Britain and India should reduce barriers to trade. Britain believed the best barrier imposed by India was restrictions on service industries, where Britain was strong.

The prime minister said: “We discussed today about how we should always both be staring at how we reduce the barriers to investment in our countries. Specifically, the British have said we will usher in a same-day visa service for Indian business. We made absolutely clear there isn’t a limit at the selection of Indian students that could study in British universities, as long as they have got an area and an English-language qualification.”