David Cameron has pledged to create a "modern, dynamic partnership" with India after welcoming Prime Minister Narendra Modi to Downing Street.
At a joint press conference, the Prime Minister admitted that links between the countries had been "imprisoned by the past" up to now.
But as the leaders unveiled £9 billion of business deals, he insisted it was time to "set this relationship free".
Mr Cameron also played down criticism of Mr Modi's record as chief minister of Gujarat - including over 2002 riots where more than a thousand Muslims were said to have died - pointing out that he had an "enormous mandate" from the Indian people.
With noisy protests taking place outside Downing Street, Mr Modi - the first Indian premier to visit Britain in nearly a decade - was brought into Number 10 via a back route instead of coming through the front gates.
The two men shook hands on the steps, before holding talks with their ministers around the Cabinet table.
At a press conference in the opulent surroundings of the Foreign Office's Locarno Room later, Mr Cameron hailed a "real opportunity to open a new chapter in the relationship between our two countries" and develop "a more ambitious modern partnership" politically as well as on the economy and defence.
British and Indian companies would be announcing new collaborations worth a total of more than £9 billion during the three-day visit, he said.
Mr Cameron said the UK should be India's "number one partner" in raising finance for Mr Modi's plan to create 100 "smart cities" across the country, with the City of London establishing itself as the world's centre for trading in India's rupee currency.
This process was beginning with the issuing of £1 billion worth of bonds in London, including the first-ever government-backed rupee-denominated bond to be issued internationally, said Mr Cameron.
Amravati, Indore and Pune are three of the cities taking part in Mr Modi's smart development programme, and Mr Cameron said he hoped British firms would get a share of the planning, design and construction work involved. Indian and British scientists will work together in a new £10 million research collaboration into low-cost, low-carbon energy sources for the smart cities.
Britain is already the largest investor in India among G20 countries while India invests more in the UK than it does in the rest of the EU combined.
"I think it is time to set this relationship free from these misconceptions and from the past," Mr Cameron said.
Mr Modi flatly rejected criticism of his record in Gujarat and allegations of reduction in civil liberties since he came to power.
"India is a land of Gandhi and therefore there is something that is deeply entrenched in our culture, our traditions, which is that we are not accepting anything that is having to do with intolerance," he said, speaking through an interpreter.
"Any incident that happens is a serious incident and we do not tolerate these incidents at all."
He denied that he had been blocked from coming to Britain in 2002, saying he wanted to "correct this wrong perception".
Asked whether he was worried about controversy surrounding Mr Modi, Mr Cameron said: "I am pleased to welcome PM Modi here. He comes with an enormous mandate from the people of India who made him prime minister with a record and historic majority.
"As for what happened in the past there were legal proceedings, there were also ... representations from the British government at the time.
"We are now discussing the future partnership between Britain and India.
"Both of us are backed by our countries for this parliament to work together and strengthen the partnership that we have."
Addressing the Prime Minister, MPs, peers and members of the UK's Indian community in the Royal Gallery of the Palace of Westminster, Mr Modi said: "This is a huge moment for our two great nations.
"We must seize our opportunities, remove obstacles to co-operation, instil full confidence in our relations and remain sensitive to each others' interests. In doing so we will transform our strategic partnership to make this relationship count as one of the leading global partnerships."
Mr Modi - the first serving Indian PM to make a speech in Parliament - said the history of the two countries was so closely intertwined that "there are many things on which it is hard to tell any more if they are British or Indian".
He cited Tata-owned Jaguar cars, Brooke Bond tea, curry and cricket, and told his audience that "even in India, every young footballer wants to bend it like Beckham".
Mr Modi said that India's future represented "the destiny of one-sixth of humanity" and that it was inevitable that its economic relations with Britain would "grow by leaps and bounds".
He said India wanted to see more trade and investment and would "open doors" to service sector companies and work together with the UK on civil nuclear energy and the development of solar power.
He called for the UK's support in obtaining a comprehensive United Nations convention against international terrorism and achieving a deal on climate change at next month's international conference in Paris.
Welcoming Mr Modi to Parliament, Commons Speaker John Bercow said India was a "standing rebuke" to sceptics who believed democracy could not work in a country of hundreds of millions of inhabitants belonging to a wide variety of ethnic and religious groups.
But he pointedly raised the concerns over free speech and equal rights being voiced by protesters outside the building, telling Mr Modi: "To rout the disbelievers completely, however, democracy has to demonstrate that it can respect free speech and incorporate a true diversity of creeds, faiths and orientations without diminishing or disrespecting any of them."
Simon Walker, director general of the Institute of Directors (IoD), warned the " vote of confidence in the British economy from one of the world's most important developing nations" risked being undermined by immigration policy.
"At a time when we are rolling out the red carpet for world leaders, we must make sure we are not closing the door behind them," he said.
"The Government's immigration policy is currently undermining our claim to be an open, trading nation.
"The IoD has joined calls for a Comprehensive Immigration Review to ensure government policies balance public concerns with the needs of business.
"International students should be removed from the numbers immediately. The public do not see them as immigrants and they underpin the strength and vibrancy of Britain's world-leading education institutions.
"But anti-immigration rhetoric and restrictive post-study visa rules are deterring students, particularly in India, from coming to Britain. The number of Indian students heading to Germany has doubled in the last five years, while the number coming to Britain has halved. This hurts our universities now and will damage our economy in the future."
Allan Hogarth, head of policy at Amnesty UK, said: "The UK needs to do more than unfurl the red carpet for yet another world leader, Mr Cameron must raise some red flags on human rights concerns too."
Mr Hogarth said there was a "fevered crackdown on critics under way in India, with more than 10,000 non-governmental organisations (NGOs) being ' de-registered' to prevent them from receiving foreign funding, and Greenpeace last week having its licence to operate cancelled.
"Mr Cameron should speak out for the people Mr Modi is so intent on silencing and make it clear that how a country treats its NGOs is a litmus test for their international standing," he said.
Greenpeace campaigner Areeba Hamid said: "If Modi is really committed to freedom of thought, the first thing he should do is to stop his home minister's campaign to shut down Greenpeace and other groups for simply taking a different view from the government. India is indeed a vibrant democracy with a robust constitution and a proud history of tolerance, but the home ministry seems to be on a mission to make the world forget about that."
Addressing business leaders and politicians at London's Guildhall, Mr Modi said India and the UK could make each other's dreams a reality.
Promising a "transparent and predictable" tax regime, he said his country had " recently been cited as the most attractive investment destination by Ernst and Young".
"Ours is the country of vibrant youths and a rising middle class," he said, adding: "We welcome your ideas, innovations and enterprises."
Mr Cameron said: "The future of India is the future of one sixth of humanity.
"These are exciting times for an extraordinary country and a leader of great vision."
The theme of co-operation between the two countries was extended to the menu for dinner at the Prime Minister's official country retreat Chequers, where Mr Modi is spending the night.
A starter of British Autumn Salad of Beets and Roots was followed up by a Porcini Mushroom Pulao, Tarka Dal and Kachumba Salad - with Mango Pudding to finish.
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