David Cameron has voiced his determination to make it easier for Indian businessmen and students to work, study and invest in the UK as he arrived in Mumbai at the head of the largest trade mission ever to travel overseas with a prime minister.

But Mr Cameron made clear that in return, he wanted India to tear down outdated barriers to investment to help UK-based companies in areas such as insurance and banking to establish a foothold in the fast-growing economy.

Speaking on the first day of his second visit to India as PM, Mr Cameron revealed he was talking to the government in Delhi about the prospects for a new corridor of development between Mumbai and Bangalore, featuring new towns and infrastructure, which could provide opportunities for British planners, architects, construction firms and finance specialists.

Mr Cameron announced the creation of a new "same-day" visa service for Indian businessmen, in response to unhappiness with the current system which can take three days or more to process applications. And he said there was "no limit" to the number of Indians who would be allowed to study at UK universities and stay on in graduate-level jobs after they qualified.

Speaking to workers at the Mumbai headquarters of the Anglo-Dutch Unilever group, Mr Cameron said: "Britain is one of the most open, easy-to-invest-in countries in the world. We are incredibly welcoming. I think, in return, we should be having a conversation about opening up the Indian economy, making it easier to do business here, allowing insurance and banking companies to do more foreign direct investment into the Indian economy.

"There are still many rules and regulations in the Indian economy associated with how you did things in the past which, if you change them, will make your economy grow and deliver more jobs, more wealth, more prosperity across your country. It's a good to have, but it goes both ways. We should look at the things we need to do to take our barriers down, and we hope your government will do the same."

Mr Cameron is accompanied on his three-day trip by a delegation of more than 100 representatives of major corporations, small businesses and academic institutions, as well as football's Premier League, the London Underground and nine parliamentarians.

He told his audience in Mumbai that he wants Britain's partnership with India to be "a really special relationship" for the 21st century. "Britain wants to be your partner of choice," said Mr Cameron. "We think there are huge ties of history and language and culture and business, but we think we have only just started on the sort of partnership we could build."

In a round of TV interviews in Mumbai, Mr Cameron rejected suggestions that his desire for a "special relationship" with India was not reciprocated in New Delhi, as prime minister Manmohan Singh is yet to visit him in the UK. Mr Cameron said: "I think the signs are very good. Half of Indian investment into Europe comes to Britain and Britain is now the largest European investor into India. I think the basis for that special relationship and partnership is absolutely there. This is going to be the third largest economy in the world by 2030 and I want to make sure it is British firms that are helping to build those hospitals, construct those roads, provide those universities, and we want a real exchange between our countries."

Mr Cameron later laid a wreath at the memorial to the 16 Indian police officers who died in the terror attacks in Mumbai in 2008. The Prime Minister bowed his head in respect before the memorial as an honour guard played the Last Post. Some 164 people were killed in a series of 12 co-ordinated shooting and bombing attacks across Mumbai, which were blamed on terror group Lashkar-e-Taiba.