Three Tory MPs broke away to join Labour MPs in the newly formed Independence Group in protest at the government’s perceived lurch to the right.
Anna Soubry, Heidi Allen and Sarah Wollaston are opposed to leaving the EU and claim the party is ‘in the grip of’ Brexiters and the DUP.
Mr Tugendhat, who campaigned and voted to Remain, told the Times: “We all stood on manifestos that said we would honour the result of the referendum.
“I do respect the democratic will of those who elected us to serve because that is the way of getting a deal over the line. I wish they would do the same and I am sorry they won’t.”
The MP is chairman of the Foreign Affairs Committee and will be at the forefront of dealings with European countries after Britain officially leaves the EU on March 29.
But he is well-known for campaigning on issues within his constituency, and he said: “We can speak about Europe all we like but the truth is people care about schools, buses and how they will get to work.
“I am constantly talking to people who care about the future and not the past, and we have to make sure that future is about growth, ideas and opportunities.
“Teams work and individual action tends not to. The truth is that all politics is about co-operation and compromise.”
Last week Mr Tugendhat’s party colleague in Tunbridge Wells, the Business Secretary Greg Clark, said he and two other Cabinet colleagues would defy the Prime Minister Theresa May.
They told the Daily Mail that they would vote against the government in a bid to delay the deadline to leave the EU rather than ‘crash out’ with a no-deal.