Britain will introduce same-day visa service for Indian businessmen wanting to invest there, Prime Minister David Cameron announced on Monday as he sought a "special relationship" between the two countries, saying it is about the future for which sky is the limit.

Out to woo Indian students, Cameron also said there would be no limit on the number of students from here studying in his country.

"I want Britain and India to have a special relationship....This is a relationship about the future, not the past," Cameron said in his first public engagement here —  an interaction with the staff of Hindustan Unilever, the Indian unit of British consumer products' giant, Unilever.

Cameron, who landed this morning in the country's financial capital, his first port of call, during his second visit to the country in less than three years after assuming office, also announced his country would introduce a same-day visa service for businessmen, in an effort to encourage Indian businesses to invest in Britain.

"We have the biggest visa operations anywhere else in the world right here in India. I announce that we are going to introduce for businesses a same-day visa service to those who want to come to our country and invest...," Cameron told India Inc at Hotel Taj, the country's hospitality icon.

Cameron is accompanied by the largest-ever business delegation to have left the British shores, as part of efforts to bolster economic ties with India.

The British premier, whose visits comes amidst the raging storm over AgustaWestland chopper deal, described India as one of the "great phenomena" of the century whose enormous growth is going to make it the third largest economy by 2030.

Cameron will fly to Delhi tomorrow for talks with Prime Minister Manmohan Singh on a range of issues. The Indian side during the talks is likely to seek more information from Britain on alleged kickbacks in the Rs 3,600 crore VVIP chopper deal.