Prime Minister David Cameron has pledged a "same-day" visa service for Indian businessmen, who want to invest in the UK instead of the current requirement of three days or more to process applications.

"Britain is one of the most open, easy-to-invest-in countries in the world. We are incredibly welcoming," Cameron told an audience of workers at the headquarters of the Anglo-Dutch Unilever group in Mumbai.

"I am very proud of the fact that it is an Indian company, Tata, that makes the Jaguars and Land Rovers that are taking the world by storm. They also roll most of our steel and own Tetley Tea - and you don't get any more British than Tetley Tea.

"I am very proud of that. Britain is an open economy and we encourage that investment".

The British prime minister was on a three-day trade visit to the world's second-fastest-growing economy, leading a delegation of more than 100 business leaders, ministers and MPs.

Britain has the largest visa operation in the world in India which accounts for 400,000 visa applications a year, and the UK is currently granting visas to 90 percent of the total applicants, Cameron said in an earlier interview to Indian daily the Hindustan Times.

"I'm also determined to ensure that the service we offer to Indian businesses encourages them to come and invest in Britain," Cameron said.

"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".

At present, India is among the top five investors in Britain with more than 700 Indian companies having operations in the country. However, British companies BP and Vodafone are two of the largest foreign investors in India.

Trade between the countries is expected to double to around £20bn ($31bn, €23bn) by 2015.

India has recently opened up its mammoth retail market to foreign investment, allowing foreign retailers to own a majority stake in a domestic retailer. In line with that, Cameron is expected to present the case of British retailers such as Tesco, who want to open stores in the country, to his counterpart Manmohan Singh.

Tesco, which has previously partnered with India's Tata & Sons to open 50 hypermarkets in India, will make a decision on the size of its investment in the country following Cameron's representations as part of the trade mission.

Britain is also trying to persuade India to buy Eurofighter Typhoon jets after French president François Hollande and Singh failed to finalise a $14bn deal to buy 126 French Dassault Rafale fighters.

The delegation includes defence manufacturers such as Eurofighter-maker BAE Systems, EADS UK, Rolls Royce and Thales UK.

The French president paid a two-day visit to India last week, amid competition for business in the country which is set to spend about $1tn on infrastructure over the next five years.

Earlier, Cameron said that the two countries can make one of "the great partnerships of the 21st century".

"We obviously have strong ties of history, language and culture but what's really exciting is the still untapped potential of our relationship.

"I'm in no doubt that India is going to be one of the great success stories of this century - a rising power in the world. And I want Britain to be one of your partners as you grow and succeed".