David Cameron voiced his determination on Monday 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But Cameron made clear that in return, he wanted India to tear down outdated barriers to investment to help UK-based companies in areas like insurance and banking to establish a foothold in the fast-growing economy.
Prime minister David Cameron holds a Q&A session with Unilever employees at their headquarters in Mumbai, India
Speaking on the first day of his second visit to India as PM, 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.
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, Cameron said: "Britain is one of the most open, easy-to-invest-in countries in the world. We are incredibly welcoming.
"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.
"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 doo 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."
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 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."
Britain was "rewriting the rules" in response to Indian business and government calls for easier access to high technology, he said.
And he added: "We are looking with your government at whether we can open up a whole corridor between Mumbai and Bangalore of growing towns and developments and work and plan that with you.
"With me, I have got architects, planners and private finance experts who can work out a complete solution, putting together all the things you need to have that infrastructure."
On providing new infrastructure, Cameron said his main advice was to "start now", rather than delaying construction for years.
He cited the example of the London Underground, which deteriorated for decades for lack of investment in upgrades.
"One thing I would say is, if you know you have got to build new infrastructure, even though you know it is going to take many years, start now," he said.