At Prime Minister’s Questions, Gainsborough MP Sir Edward said: “Apparently the Government is thinking of relaxing visa controls from India in order to get a free trade deal.
“Whilst a free trade deal is valuable in itself, we should not be held to ransom.
“Would he agree with me that our new, working class voters, who voted Brexit, did not vote to replace immigration from Europe with more immigration from the rest of the world - anymore than when they were told that they would take back control, we would lose control of the Channel?
“So, will he convince us, that he is determined to connect to our supporters and control immigration.”
Mr Johnson responded “yes” but stressed he did not “recognise the account that he has given at all”.
He added: “We don’t do free trade deal on that basis.”
He insisted that net immigration since Brexit had gone down and then sought to turn the focus of the row onto Labour, claiming it wanted to “release uncontrolled immigration”.
However, Tory MPs are warning of a backlash from voters over the Government’s failure to stop thousands of people, including families with children, from risking their lives in flimsy, unseaworthy inflatables to cross the Channel from France to Britain.
Mr Johnson said the Borders Bill, currently in the Lords, would allow the Government to “properly take back control” and to stop illegal immigration.
The Leave campaign made controlling immigration a key part of its bid to sway voters, including suggesting that Turkey joining the EU could lead to huge numbers of migrants coming to Britain.
The Government’s hopes of a quick free trade deal with the US, heavily-touted during the Brexit campaign, have also evaporated after Joe Biden became US president and the deadlock with the European Union over the Northern Ireland Protocol.
Experts also say that the free trade deals struck so far since Britain left the EU will not offset the loss in trade with the European bloc.
Ministers have stressed that Brexit has allowed the UK to respond more swiftly to the Covid pandemic, particularly in getting approval for vaccines.
Britain has had a world-leading jabs roll-out.