David Cameron has arrived in Mumbai at the head of the largest trade delegation taken overseas by a prime minister, on a mission to "open doors for British business" in India.

Among the party of more than 100 joining Mr Cameron on his second visit to India as PM were representatives of major companies like Rolls-Royce, BAE Systems and BP, small businesses, universities, football's Premier League, the London Underground and nine parliamentarians.

Mr Cameron wants to use the three-day visit, during which he will meet prime minister Manmohan Singh and president Pranab Mukherjee, to forge closer links between British business and one of the world's fastest-growing economies. Expected initiatives to encourage trade include an easing of visa conditions for Indian businessmen visiting the UK.

In an interview shortly before arriving, Mr Cameron addressed business concerns about the difficulty of obtaining visas, telling the Hindustan Times: "I think there's more we can do here and that's an area where I hope we can put an even more attractive offer on the table during this trip."

He will confirm plans for a new pan-India network of British business centres, due to open by 2017 backed by £8 million of Government money, and is expecting deals to be sealed with Indian investors which will create more than 500 new jobs and safeguard 2,000 more in the UK.

But he is also hoping to get to know India better, telling the Hindustan Times he intended to sample some curries - which he likes "pretty hot" - in the home of the spicy dish, and catch some Bollywood movies during his flights.

Speaking to the paper, he faced questions over the uncertainty felt in the Indian business community about Britain's future as a "gateway to Europe" following his promise of a referendum on European Union (EU) membership and concerns that his ambition of getting net immigration down to "tens of thousands" a year will make it more difficult for businessmen and students to come to the UK.

But he rejected suggestions that his drive to double UK-India trade by 2015 had lost momentum since he made the Asian sub-continent his first foreign destination after taking power in 2010, insisting he was "on track" to meet the target.

Mr Cameron is expected to use his visit to explore the prospects for reviving a bid to sell the Eurofighter - made by a UK-German-Spanish-Italian consortium including BAE Systems - to the Indian air force, after President Francois Hollande failed last week to clinch the deal for France's Dassault Aviation, which was previously chosen as preferred bidder.

He will also send a message to Indian students that there are "no limits" on the number who can come to learn at UK universities or stay on in Britain in graduate-level jobs. And Transport for London is expected to agree close co-operation on transport planning with authorities in both Hyderabad and Mumbai, where there are plans to build a 90-mile underground train network.