But, in the Commons, the strategy was attacked by Edward Leigh, a Brexit-backing Conservative, who told him: “Whilst a free trade deal is valuable in itself, we should not be held to ransom.
“Would he agree with me that our new working-class voters who voted Brexit did not vote to replace immigration from Europe with more immigration from the rest of the world?
In response, the prime minister denied there was any such plan, telling Sir Edward: “We don’t do free trade deals on that basis.”
Instead, he boasted of lower immigration, adding: “I can tell him actually that net immigration, since we took back control, has gone down and we will continue to make sure that we take advantage.”
Narendra Modi, the Indian prime minister, is believed to have made easier immigration to the UK a red line for closer trade ties – although Delhi has been opposed to free trade agreements for other reasons.
The government is under pressure to achieve a trade deal with a major country after the US shelved talks, leaving low-value Australia as the only new partner found since the UK left the EU.
One option thought to be under consideration is a scheme similar to that agreed with Australia, to allow young Indians to move to work in the UK for up to three years.
Another would be to cut visa fees for students and allow them to stay in Britain for a period after they graduate, The Times reported.
There could also be reductions in visa fees for both work and tourism, it said. At present it can cost an Indian citizen up to £1,400 for a work visa, while students pay £348 and tourists £95.
For British tourists travelling to India the fee is £110, while a one-year business visa costs £165.
The country is predicted to become the world’s third largest economy by 2050 but it has always had a protectionist outlook, with hefty tariffs on imports.
Last May, the UK and India announced only an “enhanced partnership”, pledging to create 6,500 jobs in the UK through investments centred on health, technology and vaccine development.
In the same week, the EU threatened to steal a march by announcing its own trade deal talks were about to start.