One week after French President Francois Hollande voyaged to India to seek greater trade relations, UK Prime Minister David Cameron and a large trade delegation have commenced a three-day visit to the former "jewel in the crown" to make Britain’s case for closer ties with India.

Accompanied by an array of British business leaders, including officials from BAE Systems (LON: BA), Rolls-Royce (LON: RR), and London Underground, Cameron has also suggested that the British government will make it easier for Indian students and businessmen to obtain visas to visit the UK.

"We want to make sure that we are attracting ... the best and the brightest. And in terms of our visa operation here in India, it is the biggest one we have anywhere in the world. Nine out of 10 of those who apply for a visa get one," he told Indian TV.

"We are introducing today a same-day visa service for business people who want to come to Britain for linking up their businesses for trade and other things like that.”

Cameron, making his second official trip to India as prime minister, also called for the formation of a 21st-century “partnership” between India and Britain. He has already targeted a doubling of UK-India trade by 2015.

"India's rise is going to be one of the great phenomena of this century and it is incredibly impressive to see,” Cameron told an audience in Mumbai.

"Britain wants to be your partner of choice. We've only just started on the sort of partnership that we could build. As far as I'm concerned, the sky is the limit."

Cameron is also slated to meet with Indian Prime Minister Manmohan Singh and President Pranab Mukherjee in New Delhi.

James Landale, deputy political editor at BBC, noted that while trade between UK and India has been increasing in recent years, it started at a low base.

“Belgium trades more with India than we [UK] do,” Landale wrote. “We trade more with North Rhine Westphalia than with India. So when Mr. Cameron talks of ‘untapped potential’ and there being ‘much more to do,’ he is speaking with some degree of understatement.”

Landale noted that since Cameron’s first trade trip to India three years ago, few deals have been engineered between UK firms and India – most notably, the New Delhi government contracted to buy fighter jets from France, rather than from Britain.

“This may be the largest prime ministerial delegation ever, but it arrives in Mumbai on bended knee,” he said.

Cameron likely realizes that India plans to spend some $1 trillion on infrastructure over the next five years -- and he would surely love for British firms to win as many of those impending contracts as possible.

"We cannot rely merely on sentiment and shared history with our trading partners," Cameron said in London prior to his departure. "We have to get out there, make the case for Britain and open doors for British business."

Some observers in Britain are scratching their heads over Cameron’s offer to allow Indians easier visa access to Britain, considering the Conservative Party's longtime hostility to immigration.

Alana Letin, a columnist at the Guardian, suggests that Cameron is making a sharp distinction between Indian students and businessmen and economic refugees from Eastern Europe, particularly Romania and Bulgaria, who may soon flood into Western Europe upon the relaxation of cross-border movements.

“An English-educated Indian professional may be more acceptable than a white, jobless Bulgarian or Romanian,” she wrote.

“This is exactly on point as we witness David Cameron's rush to India, a country whose economic rise he described as ‘one of the great phenomena of the century.’...  Back in the UK, the imminent arrival of Bulgarians and Romanians with new EU rights is being painted as a make or break electoral issue. They are the victims of a ‘xeno-racism’ that holds impoverished strangers, including whites, in its sight. In contrast, Indian students with the cash to pay premium fees to study at British universities will, according to Cameron, have the red carpet rolled out and will not, he has claimed, be subject to limits on how long they can stay and work.”

Letin also suggests that Indians enjoy a far better image in the UK than Eastern Europeans and others.

“Cultural stereotypes abound,” she stated. “Indians – not Pakistanis mind – are deemed hardworking and resourceful with infinite admiration for the UK and its traditions. Colonialism is rewritten as a ‘special relationship.’ Indians (Hindus) assimilate into the British way of life, speak English, and are religious moderates. They are not a drain, rather an opportunity for investment in an ailing British economy.”

She adds: “This is the message that Cameron is sending: We will tolerate those who can benefit us, but not those who fail to make us prosper.”