David Cameron is eager to show that he can break with the past and chart new avenues – what with the coalition with the Liberal Democrats and talk of the "big society" reversing decades of centralised government power. But as he heads to India accompanied by a cricket squad of ministers and businessmen, he would do well to read up on a bit of history – and in particular, on the letter that Queen Elizabeth I gave to John Newbery, one of the first Englishmen to visit India.

Dated February 1583, it was addressed: "To the most invincible and most mighty Prince, Lord Zelabdim Echebar, King of Cambaia; Invincible Emperor, etc." The letter explained that Elizabeth's countrymen liked to trade, that they thought this would be of mutual benefit, and that they were willing to travel great distances for this purpose. The letter went on to speak of the Indian Emperor's "humanity", and of how the English Queen would be "greatly beholden" if he would treat her subjects "honestly" and grant them "such privileges as to you shall seem good".

Elizabeth was not well informed about India. She had the wrong name for the Indian monarch and was mistaken about his title. He was Jalaluddin Akbar, one of the great Mughal Emperors, whose domain extended far beyond "Cambaia". For good measure, she also misspelled the name of this port in modern-day Gujarat, on the west coast of India – it was, in fact, Cambay – though she could have claimed some kind of credit, if only because it was along the town's waterfront that, 130 years later, British sailors first introduced cricket to the Indians. What gives the letter real contemporary relevance, however, is that – like Newbery – Cameron and co are going to India to trade. And while Britain is no longer quite the small island threatened by Spain, then Europe's most powerful kingdom, its present economic woes do make it much more of a supplicant – all the more so, as India is convinced it is on its way to regaining its old 16th-century economic domination.

Then, the Mughals could realistically have expected to be described as one of the world's great powers – and for the next century and a half, it was India, along with China, that dominated global trade. Even in 1750, 167 years after Elizabeth's begging letter, India had 24.5 per cent of the world's manufacturing output – with China leading the field with 32.8 per cent while the United Kingdom was barely visible with 1.9 per cent. It was another seven years before Robert Clive's decisive victory over the Nawab of Bengal on the banks of the Bhagirathi River at Plassey converted the British from traders to rulers and changed everything.

Modern India has still some way to go to regain its once-lofty position but it is growing at over 8 per cent a year, and the recession that haunts the West is for most of its people just a series of media images from another part of the world. India has had no need to bail out its banks or adjust to an age of austerity. True, as in the 16th century, vast inequalities of wealth remain – with just under half the population of 1.2 billion living on less than $2 a day. But a thriving middle class of 400 million people is constantly seeking to lift an economy already ranked 11th in the world. And in marked contrast to the ageing societies of China, Japan and Europe, the prospects for growth are further fuelled by an increasingly young population – with 70 per cent of Indians under the age of 35. And all this is complemented by a certain political and historical maturity.

I was made aware of this on a recent trip to the heartland of northern India. The trip took in sites such as Nalanda, the university that dates to the fifth century BC and claims to be the oldest in the world. It included Bodhgaya where, under an ancient Bodhi Tree, a little-known prince called Siddharta found inspiration after years of meditation and became Buddha, and Sarnath, where Buddha preached his first sermon.

At every place, the guides took pains to point out the destruction that the various invaders, many of them Muslims, had inflicted. But almost in the next breath they went on to praise the British, who in many cases had rescued the ruins, indeed made the Indians aware of their history. This praise extended even to Lord Curzon – who, in 1917, told the British War Cabinet that it would take Indians 500 years to learn how to rule themselves. His reign as viceroy ignited the first great nationalist agitation against British rule. But he also did much to protect ancient Indian monuments.

This Indian ability to move from touchiness about the Raj to a more confident, measured view of its impact has been helped by the economic success of Indian businesses and the mark they are making on the international scene. In the India of my childhood, hawkers in Mumbai would shout "novelty, novelty", holding out the foreign goods we so desired but could not get. For my generation, everything foreign was good and we could not wait to escape India. But now Indians can see on their screens their fellow Indians emerging as giants of world business – particularly in Britain.

Lakshmi Mittal, head of the world's biggest steelmaker, is top of the Sunday Times Rich List. And another Indian, Anil Agarwal of the mining group Vedanta, is in the Top 10. Even more pleasing to Indian eyes is the Tata Group's success. In a country where businessmen and politicians are expected to be corrupt, the Tata name is magic. It represents well-run businesses which know how to make money, treat their employees properly and set standards in business probity. Tata stories are part of Indian folklore.

At the beginning of the 20th century, a member of the Tata family was refused entry to a whites-only British club in Mumbai which had a sign saying "Indians and dogs not allowed". The Tata response was to build the Taj Mahal hotel and put up a sign saying "British and cats not allowed". Apocryphal as the story may be, the Tata legend was augmented when they became the first steelmakers in India, defying the Raj official who promised to eat any steel the family produced. As the Tatas have taken over such iconic British brands as Jaguar and paraded their Nano city car on British streets, Indians feel that the awful ghost of the East India Company, the trading entity that conquered India, has been exorcised.

This was illustrated recently when there was speculation that Anil Ambani, one of the richest men in India, might buy Liverpool football club. There was much debate on Indian television of the merits of owing a Premier League club. One participant suggested it was payback time to the British for the East India Company. The presenter cut in sharply, saying: "We paid them back a long time ago. I thought the Indians owned most of the British businesses worth having. We don't need to buy a football club to demonstrate that."

The rest of the panel roared with laughter, showing the confidence of modern India and how it views its old imperial master. It should be noted that it is an attitude further shaped by the fact that Britain, after 200 years of dominance, is no longer the only foreign power that counts.

The Indian leadership, led by Prime Minister Manmohan Singh, that Cameron will meet in Delhi is still largely English-educated. Singh is a Cambridge graduate who was tutored by Sir Alan Walters, Mrs Thatcher's economics guru. But Singh is now 77 and his generation is on its way out.

A younger generation mainly educated in the US is waiting to take over. It includes Jyotiraditya Scindia, the 39-year-old minister of state for commerce and industry, and Sachin Pilot, the 32-year-old minister of state for communications and technology. Scindia is of the royal family of Gwalior which, during the Raj, would not have been allowed to deal with a foreign power except with British blessing; now he brings to Delhi the skills he acquired at Harvard and Stanford. For his part, Pilot went to Pennsylvania.

The 39-year-old Rahul Gandhi, who is being groomed to take over from Singh, was educated at Cambridge but also at Rollins College, Florida – a fact that would have been anathema to his great grandfather Jawaharlal Nehru. A product of Harrow and Cambridge, Nehru used to rile his British jailers by singing Harrow school songs. After becoming free India's first Prime Minister he maintained the British connection. He accepted pleas from Churchill and Attlee that India should remain in the Commonwealth, overturning the long-standing policy of his Congress party that India should leave. While he kept secret his affair with Lady Mountbatten, wife of the last Viceroy Lord Mountbatten, he looked forward to his airmailed copy of the weekly New Statesman and loved visiting London. By contrast, he distrusted America and made no secret of his desire to limit American influence in India.

Some Indians still have a schizophrenic attitude to the United States, summed up by Prannoy Roy, who runs NDTV, India's most-successful news channel. "We Indians love to say, 'America leave – but take us with you.'" But this is changing due to the presence of a large and successful Indian diaspora in America. It has also been helped by Pakistan, long regarded as America's "client" in the region, now being seen as a failed state. All this has moved India closer to America and, the Communists apart, most Indian leaders are now keen to make up for half a century of neglect.

An interesting illustration of the American influence is in the launch of the Indian Premier League – the Twenty20 cricket competition known as the IPL – and is well summed up in the story of Lalit Modi, the man who created it but has since been drummed out of the game for alleged misdeeds.

Modi has both a US degree and a US conviction. In 1985, while still at university, he was convicted of abduction and possessing cocaine. He escaped jail on a plea bargain, agreeing to five years of probation and 100 hours of community service – and once he had graduated, he persuaded an American court to let him return to India on health grounds.

While the English had invented Twenty20 cricket but done nothing much with it, Modi, making the most of India unexpectedly winning the first Twenty20 World Cup, launched the IPL in the spring of 2008. The name IPL may echo the title of the English football's Premier League but many of Modi's ideas, such as creating city-based sports franchises, were borrowed from American sports. At IPL matches, Modi introduced blonde pom-pom girls, who gyrate every time a four or a six is hit – celebrations familiar to American followers of sport but never before seen in cricket.

The IPL emphasised that India is the powerhouse of cricket, providing 80 per cent of the world game's income, thus allowing Modi to sell the television rights for over $1.6bn. It also underlined that when it comes to ideas, these days India looks to America.

Even Modi's subsequent fall from grace had an Americanised feel to it. Under investigation for tax evasion, money laundering, bogus offshore companies and sweetheart deals, Modi's IPL gave the impression of having operated in a manner similar to the way that business was run in unregulated 19th-century America – with no corporate governance and any deal, however dubious, permissible.

Ironically, Modi's problems came about because of his clash with another Indian high flyer who has spent much of his life in America. This was Shashi Tharoor, who was educated in the US and then worked for the UN for nearly 30 years, just missing out on becoming Secretary General to the South Korean Ban Ki-moon. Last year Tharoor was parachuted in to contest the safe Kerala seat of Thiruvananthapuram and was made a minister of state in the Foreign Office. Evidently, the Congress leader Sonia Gandhi saw him as the sort of man to be part of the coterie around her son Rahul, when he takes over as Prime Minister.

But Modi's tweeting about Tharoor's involvement with a franchise in Kochi, a coastal town in Kerala, raised questions about the minister's judgement and forced his resignation. For good measure, the Indian Prime Minister was in the White House when the story exploded and had to take time off from meeting President Obama to deal with it.