Theresa May was personally responsible for stalling talks on an EU free trade deal with India, because she was obsessed with controlling immigration, according to former business secretary Vince Cable.

The prime minister will travel to India next month in a bid to lay the groundwork for developing a new trading relationship, after Britain leaves the EU.

But Cable, who was closely involved in liaising with Brussels as business secretary in the coalition, said a key sticking point in years of unsuccessful negotiations between India and the EU was May’s refusal to compromise on immigration.

Cable said India had been keen to expand “Mode 4” market access: the ability to bring in staff – Indian IT experts, for example – as part of trading in services. “What the Indians were asking for was very modest – and these are the kinds of people who, if we were being rational, we would want to have in the country,” he said.

But he said May, then the home secretary, refused to compromise because “she was obsessed by her target” of bringing down immigration.

Cable said there were other issues at stake in the complex trade deal negotiations, which began in 2007 but were never completed, including Britain’s desire to win better access to the Indian financial services market. But he said objections to migration were crucial to the failure of the talks’ progress.

Cable said: “I and other ministers would come back and say, ‘the Indians want improved access on Mode 4,’ and the answer would be, ‘Not on your nelly, we’re not doing anything on this.’ The message would go back to the EU that the British were not willing to budge.” He added: “They [the Home Office] were very obstructive.”

The former business secretary said post-Brexit Britain would continue to struggle to complete a trade deal with India, unless May was willing to take a more flexible approach on immigration. He said: “If you’re talking about trade in services rather than trade in goods, it involves people moving around – but they’re pathologically opposed to people moving around.”

Some pro-Brexit ministers, including the international development secretary, Priti Patel, suggested during the referendum campaign that extricating Britain from the EU could eventually result in higher levels of migration from non-EU countries, including India. But May has made clear that she regards controlling all migration as a central benefit from leaving the EU.

Prof Anand Menon, director of thinktank UK in a Changing Europe, said it was naive to think that once Britain has left new trade deals would be easy to strike. He said: “The fact of the matter is, in some circumstances, the EU’s not the stumbling block – we are.”

Menon said a 2013 Home Office proposal to force migrants from some countries, including India, to post a £3,000 bond, had been bad for perceptions of the UK, although it was never enacted. “The mood music in the Indian press was: ‘These people want to do deals with us but they don’t like our people,’” he said.

Announcing her visit to India, the prime minister said: “As we leave the European Union, we have the chance to forge a new global role for the UK – to look beyond our continent and towards the economic and diplomatic opportunities in the wider world.”