The Indian High Commission in London has disputed allegations made by the home secretary Suella Braverman that the Indian government is simply not doing enough to reverse the flow of its illegal immigrants and overstayers in the UK.

In an interview with The Spectator, Braverman said: “Look at migration in this country – the largest group of people who overstay are Indian migrants. We even reached an agreement with the Indian government last year to encourage and facilitate better cooperation in this regard. It has not necessarily worked very well.”

As part of the bilateral trade deal the UK has agreed to give more visas to Indian businessmen and women as well as students. In return, India has agreed to take back illegal immigrants and overstayers.

In her Spectator interview, Braverman indicated she was not happy with the concessions the UK was making – concessions that have the support of Liz Truss, who was involved in negotiating the trade deal with India as international trade secretary and foreign secretary. In fact, Truss made three trips to India.

Braverman said: “I have concerns about having an open borders migration policy with India because I don’t think that’s what people voted for with Brexit.”

When The Telegraph asked for a comment from the home office on the Indian High Commission’s objections to Braverman’s comments, its spokesman refused to be drawn into the controversy beyond saying: “We can refer you back to the home secretary’s words.”

The Indian Commission suggested that it was the UK side that had not honoured all its commitments under the Migration and Mobility Partnership (MMP) agreed between the two sides. It claimed all cases referred to the high commission had been dealt with. It also said that whatever agreement was reached under the trade deal would be of benefit to both sides.

In part the MMP talks about “reaffirming their determination to strengthen cooperation in the field of mobility and migration, with a view to encouraging the legal and orderly movement of students and professional skilled workers to each other’s countries, subject to the opportunities available”.

It refers to “resolving to prevent immigration abuse in both directions and to assure the return to the Participants’ countries of illegal residents who have been properly identified by the procedure set out in this MoU”.

It also includes a section about “determining to jointly take appropriate steps to prevent and suppress illegal migration, smuggling of migrants and trafficking in human beings, in accordance with respective national legislation”.

And “noting the establishment in the UK of the new Points-Based Immigration System following the UK’s departure from the European Union, which will create parity of treatment for work and study migration between all third countries, and will offer greater opportunities than hitherto to non-EEA (European Economic Area) migrants”.

The Guardian thinks Braverman has an agenda of her own. It said: “Suella Braverman has again risked upsetting No 10 after saying she has ‘reservations’ about Britain’s trade deal with India because it could increase immigration to the UK.

“Liz Truss said she wants to sign a trade agreement with India by Diwali at the end of this month. The Indian government is demanding an increase in work and study visas for Indian nationals and earlier this year Boris Johnson said the agreement would lead to increased immigration.”

It added: “Home Office statistics show that 20,706 Indians overstayed their visas in 2020, higher than any other nationality, although other nationalities recorded a higher proportion of overstayers. Of the 473,600 Indians whose visas were due to expire in the 12 months to March 2020, 452,894 are known to have left, meaning 4.4 per cent of them overstayed their visa.”

Braverman set out her stall in her speech last week at the Tory party conference.

She talked of her “mission to control our borders.

“Firstly, legal migration.

“I backed Brexit because I wanted Britain to have control over our migration and to cut overall numbers. Brexit was meant to give us a say on how we determine our own migration policy.

“But the truth is parts of our system aren’t delivering. We need to end the abuse of the rules and cut down on those numbers that aren’t meeting the needs of our economy.

“It’s not racist for anyone, ethnic minority or otherwise, to want to control our borders.

“It’s not bigoted to say that we have too many asylum seekers who are abusing the system.

“It’s not xenophobic to say that mass and rapid migration places pressure on housing, public services and community relations.

“I reject the Left’s argument that it is hypocritical for someone from an ethnic minority to tell these truths.

“My parents came here through legal and controlled migration. They spoke the language, threw themselves into the community, they embraced British values. When they arrived, they signed up to be part of our shared project because the United Kingdom meant something distinct. Integration was part of the quid pro quo.”

In some ways it was the speech of a politician with an eye on the top job.