Britain and India on Tuesday signed an accord on migration and mobility, a foreign ministry official said, as they look to deepen economic, cultural and other ties following the UK's departure from the European Union.

The pact will provide enhanced employment opportunities for 3,000 young Indian professionals annually, in return for India agreeing to take back any of its citizens who are living illegally in the UK, foreign ministry official Sandeep Chakravorty told a news conference.

The migration pact comes after the two countries announced 1 billion pounds ($1.39 billion) of private-sector investment. Talks on a full trade deal are due to begin in the autumn.

"It is our solemn duty that Indian nationals who are undocumented, or are in distress abroad and not being given nationality or residence permits, have to be taken back," Mr Chakravorty said.

Britain's interior ministry said in a statement that the deal aimed to attract "the best and brightest, and supporting people coming to the UK through legal routes, while stopping the abuse of the system and speeding up the removal of those who have no right to be in the UK".

Migration has long been a source of friction between the two countries, with a similar proposal collapsing in 2018 due to disagreements.

At the time, London claimed there were as many as 100,000 Indians living illegally in the UK, though New Delhi disputes this figure.

Tens of thousands of Indians study in the UK each year, and New Delhi has complained about a lack of employment opportunities available to them when they finish their studies.

Earlier on Tuesday, Prime Minister Narendra Modi pressed his British counterpart Boris Johnson during talks by telephone over the status of two Indian fugitive tycoons, Vijay Mallya and Nirav Modi, who are wanted by New Delhi on fraud charges and are believed to be in the UK.

Johnson said he faced some "legal hurdles" but was committed to extraditing the pair back to India as soon as possible, Mr Chakravorty added.