Sir Dominic Asquith, the British high commissioner to India, was in Calcutta for the Queen Elizabeth II Cup on Saturday. In his only interview on this brief visit, Asquith answered some questions at the Royal Calcutta Turf Club after a thrilling finish to the race for which the Queen sends a gold-plated trophy from Buckingham Palace to Calcutta through the British high commission every year. Held in association with The Telegraph, this is the longest race of the season.

This is the 66th Queens Cup. Where does it sit in the relationship between Britain and India?

The Queens Cup is a wonderful thing to celebrate. It's one of three Queen Elizabeth II Cups - there's one here, one in Hong Kong and then there's Royal Ascot... it reflects her passion for racing. But there's a more symbolic, a greater significance, I think... what we call the 'living bridge' between the United Kingdom and India. The living bridge connects the two countries, over which people and ideas and technology are going back and forth. It's not one-way traffic.

One of the things which binds us is particular interests and passions in common sports, and racing seems to be one of those. And we have that typified here. The Queen is passionate about racing, the British public is passionate about racing... six million British people attend racecourses every year, second only to football in terms of popularity. So there's something very important and very significant about celebrating that particular link. It's an example of a passion going back and forth over the bridge.

Another thing that goes over the living bridge would be education. But since Brexit happened, there's a sense among many Indian students and professionals that it might get harder and harder to get into the UK.... Is there something you would like to say to them?

Yes, very much. I would encourage everyone to read the speech that our Prime Minister Theresa May gave about two weeks ago at Lancaster House. It set out precisely what Britain's ambition was, in the context of Brexit. One of the things that she identifies as important to Britain as it relates to the wider world is that she wants Britain to be a magnet for international expertise, for innovation....

The vote on Brexit was not a vote to, as we say, put the drawbridge up, to turn our back on the world. It was very much the opposite. It was saying, we want to be active not just with Europe, we want to be active with other people in the world. And there are some people who are really important to Britain, because of the historical... but also because of the current partnership... and India's top of that list. In terms of trade, investment, shared views... you're the biggest democracy, we're the oldest democracy - that's an old cliche.

Britain is the largest foreign investor in India, India is the third-largest foreign investor in Britain. It's the second-largest contributor of jobs in the manufacturing sector among foreign investor. There are massively important Indian companies operating in Britain. India invests more in Britain than it does in the whole of the EU combined.

You met top government officials in Calcutta on this visit. So, are you 'looking East' within India?

I go around the country a lot and see the chief ministers and the key ministers in each of the state governments. Here is no exception. I had a very good meeting on Thursday with chief minister (Mamata) Banerjee, I saw the finance minister (Amit Mitra) again today (Saturday). What both sides are trying to do is work out how we can both build and collaborate to the benefit of both of us, whether in trade or investment or technology or education or research or skills, or the cultural aspects.... As West Bengal develops its economy, its urban development, its industrial expansion or its role as the entry point and exit point for trade... we will look always where British companies can participate in those projects.

The United Kingdom has a tremendous amount to offer. A lot of people at the time of the Brexit referendum said the effect on the British economy would be disastrous. On the contrary, employment levels are the highest ever, production levels are the highest ever, the rate of increase of the GDP is marked up. (Smiles) It's not as grand as the Indian GDP rate but compared to the other OECD (The Organisation for Economic Co-operation and Development) countries, it's pretty impressive.... There are a lot of reasons why Indian businesses should be looking to Britain.

Two very symptomatic things that I am delighted about in the last month or so - an agreement between our aviation ministries for opening up even more routes between India and the UK, that's really important, that's part of the living bridge; and the other is British Council recently announced almost 200 more GREAT scholarships for undergraduates and post-graduates to come to the UK, which is in addition to the 130 Chevening scholarships.

I was up in Gujarat for Vibrant Gujarat. I went to see some of the pharmaceutical companies and talk to them about some of the collaborative research that they are doing... and in really important areas - cardiovascular, Alzheimer's.

Then I was at the Institute of Neurosciences Calcutta (at Mullickbazar). A fantastic example, I mean a really fantastic example of what I call the living bridge, Institute of Neurosciences and Newcastle University have developed what CNBC has called, I think for the last two years, the best single-speciality clinic to do with neurosciences in India. I went there, it was full of people there to receive the very best treatment at a ridiculously affordable price. That's real commitment. Robin Sengupta (R.P. Sengupta) has been with the National Health Service for many, many years and he is absolutely committed to collaborate with India, to bring something back.

Edinburgh University is doing something here on wave power, tidal power, as well.

Since you mentioned Gujarat, there is a perception that certain states in India are business-friendly and some, like Bengal, are not. How would you rate the states in terms of ease of doing business?

I see a huge change throughIndia everywhere I go. Every state is enthused by this idea of ease of doing business, where they are on a particular league table as it were, and they have got clear incentives to be attractive to foreign investment and Indian investment. So I sense there is a real competition going on between states, to make sure that they are attractive and it's something that the British government feels extremely strongly about.

We are collaborating with India on Prime Minister Modi's ambition to move India up the ease of doing business World Bank league table. We do that with a variety of states, I'd be very happy if we can develop a programme here, with West Bengal. It's something Britain is extremely good at, I think we are fourth or fifth in the league. Why is it important? It is important precisely for the reason you asked that question. It creates the conditions, the atmosphere in the business sector that makes a place attractive for investment.

Finally, some people in Calcutta received strongly worded letters from the UK Home Office saying 'No right to remain in the UK' well after they had exited the UK. Is there something you would like to say about those letters?

I'm not going to comment on the letters or whether they went to the right people or not. There's a few things that I think is important to get out there. Firstly, we welcome Indian visitors warmly. The number of visas continues to increase year-on-year. The number of business visas issued to Indians is more than what we issue to China, the US and, I think, Brazil combined. That's a huge number and we welcome that.

This idea that somehow Britain is becoming xenophobic or hostile is just not true. One of the figures I really, really like is Edinburgh University has a 99.7 per cent success rate in Indian student application. That is not a figure that points to Britain not wanting Indian students!

But there is a problem in that there is a large number - I won't give the number because it's not fair, but it is a very large number, indeed the largest of all nationalities - of those who've overstayed the length of their visas. It's important to be clear, if they've overstayed the length of their visa, they are in the country illegally, and that's a serious problem. We have to find a way to address that so that those who are in Britain illegally return to their countries. So what you saw there was a reflection of the importance of addressing that particular point. If mistakes were made, mistakes were made, in terms of that they were sent to people who weren't there... that can happen, can happen certainly when the numbers are so large.

But, you know, the two points, let's address that but let's keep absolutely focused on what the market is doing. The market in terms of Indian visitors is one that is increasing and we welcome that... (We are) delighted that there are one-and-a-half million Indian diaspora in the UK who contribute a phenomenal amount to the British economy, culture, to the success of Britain. The links and business relations, the cultural connections as a result of that diaspora is in millions. That's a really powerful message for me and that's the one I prefer to focus on.