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.

In an interview with the Spectator, Braverman said Indian migrants make up the largest number of visa overstayers in the UK. The home secretary also criticised a deal with India, signed by her predecessor Priti Patel, to increase the number of illegal migrants and overstayers returned to the country, saying the agreement “has not necessarily worked very well”.

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% of them overstayed their visa.

Braverman told the Spectator: “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.”

Asked whether she would support a deal if it only involved greater flexibility for students and entrepreneurs, she said: “But I do have some reservations. 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.”

Braverman has already caused alarm in the government by saying on Tuesday she would aspire to cutting net migration to “tens of thousands” – a promise that previous Conservative governments have failed to keep.

One senior source said: “No one knows why she made those comments. That promise was used time and again to criticise Theresa May when she was home secretary.”

Braverman has also called for the UK to leave the European convention on human rights (ECHR), while government policy is to work within the convention.