David Cameron is in Mumbai to head up the largest trade delegation taken overseas by a Prime Minister and to "open doors for British business" in India.
Business leaders have said the government could be doing more to encourage Indian trade with the UK.
Despite a lack of history, many European countries enjoy better trade with the fast-growing economy, and there are concerns that recent visa restrictions for students might be preventing better ties from being formed in the future.
Special Correspondent Rageh Omar reports:
David Cameron has told the museum audience in Mumbai that Britain is taking steps under his leadership to become the "most attractive place for investment" in the world.
The Prime Minister appealed to Indian businesses and entrepreneurs to make Britain their "partner of choice".
Addressing an audience at the Chhatrapati Shivaji Museum in Mumbai, Prime Minister David Cameron has said shared commitments and the countries' close connections make Britain and India "natural partners" for trade.
Having faced many a sticky wicket at Westminster, David Cameron has taken time out from his Indian trade visit to test himself against the host country's young cricketers in Mumbai.
The Prime Minister gets the centre of the bat on the first few balls, but it is not long before his innings is over.
David Cameron is leading a major delegation of business leaders on a trip to India.
As well as making the case for British business, the Prime Minister said there would be no limit to the amount of Indian students who can study at UK universities.
ITV News Political Correspondent Carl Dinnen reports:
David Cameron has laid a wreath at the memorial to the 16 Indian police officers who died in the terror attacks in Mumbai in 2008.
Over 150 people were killed in a series of coordinated shootings and bomb attacks.
David Cameron may have been stumped at a Q&A in Mumbai earlier but he bounced back by following his own advice that exercise is the key.
The Prime Minister took a break from his trade mission in India to take part in a cricket match at the famous Oval Maidan.
He faced some ferocious deliveries from youngsters but handled them well, with former England women's captain Clare Connor saying, "he's got used to the rough surface very quickly" and adding "that's a brilliant cover drive."
Mr Cameron's middle stump eventually fell to a fast ball from a young bowler named Sachin - possibly in homage to India's cricket hero Sachin Tendulkar.
The Prime Minister said: "It was good fun and it's a great place to play. I knew I was in trouble when they brought on that third bowler though."
David Cameron has described Unilever as a "great British success story" after holding a Q&A at the company's Indian headquarters in Mumbai.
He tweeted: "At Unilever - a Great British success story here in India. I'm with a huge trade delegation to drum up business for UK."
David Cameron had a sticky end to his Q&A in Mumbai this morning when he drew a blank on Unilever products.
In the last question of the session held at the India headquarters of company, the Prime Minister was asked which of the firm’s brands were his favourite.
“I might get some of your brands wrong and mention the dishwasher liquid we use and find it is made by your competitor,” he said hesitantly.
“So I’m going to do that thing that politicians always do when they get a really tough one and dodge the question.”