Lord Howard said he would pay the Remainer a “compliment” before quickly delivering a huge Brexit swipe at the Labour Lord.
The peers were discussing the Government’s Withdrawal Bill which will soon return to the House of Lords.
Lord Howard said: “I will say this for Andrew. Let me pay Andrew a compliment.
“He has made no secret of the fact that he does not accept the result of the referendum.
“He does not want us to leave the European Union.
“I think that is undemocratic because of the referendum. I think it is arrogant.”
Lord Howard then delivered the “compliment” to Mr Adonis as he spoke on Good Morning Britain.
He said: “But at least he is straight forward and tells us what he wants.
“Unlike, I’m afraid, some people who pay lip-service to Brexit but strive to achieve something that can only be described as ‘Brexit in name only’.
“Sadly, I am sorry to say, some of those people are in the House of Commons because they were elected on a Conservative manifesto which made it crystal clear that leaving the European Union meant leaving the customs union and single market.”
Speaking later in the debate, Lord Howard said it was very clear what the British people voted for.
He said: “The Prime Minister constantly said we needed to have control over our borders.
“People have spoken, parliament must respect their decision.”
It comes as Theresa May fought off defeats on the Government’s Withdrawal Bill which threatened to keep the UK ties to the customs union and the European Economic Area.
The BBC’s Laura Kuenssberg tweeted: “Government wins. Getting there wasn’t pretty and the Government has arguably given away some of the incentive for the EU to do a decent deal in October.”