“The issue is not about visas,” Sir Keir said. “It’s about business to business engagement and investment and jobs and prosperity coming into the United Kingdom.”
The UK’s trade deal with India was signed in July after years of negotiation.
It will mean UK cars and whisky will be cheaper to export to India, and Indian textiles and jewellery cheaper to export to the UK as part of the multi-billion pound trade boost.
The deal included a three-year exemption on social security paid by Indian employees working in the UK on short-term visas.
But ministers insisted there were not wider changes in immigration policy.
The Labour government is trying to cut levels of immigration into the UK and announced a tough policy on settlement status at the party’s conference last week.
Speaking to reporters on the plane on the way to Mumbai, Sir Keir said visas “played no part” in the trade deal with India and that situation had not changed.
Asked whether the UK might consider trying to attract tech entrepreneurs in the wake of US President Donald Trump’s changes to the H-1B visa in the US, Sir Keir said the UK wanted to attract “top talent” from across the globe to help grow the UK economy, but repeatedly said there were no plans for new visa routes to India.