The staunch Remainer said there was “little doubt” that Brexit would take place and argued a second referendum on any deal would be “folly”.
Mr Clarke told an audience at the Scottish Parliament’s Festival of Politics that a “no deal” scenario with the UK crashing out of the European Union was “very unlikely”.
Asked if he thought there was any way Brexit could be averted, he said: “I’m more pessimistic than most people who were Remainers. I don’t think there is.
“The political class as a whole, leaving aside eccentrics like me, and as I say I think I was mainstream until a couple of months ago, they’ve all decided that this referendum was a kind of instruction from on high. It is the voice of the people and it can’t be challenged.
“Whether that will change, it won’t change in a hurry and I don’t think Parliament could bring itself to, they’re all terrified of the right-wing newspapers.
“They’d be accused of being saboteurs and enemies of the people if they stick to the opinions they had before the referendum.
“They did all say during the referendum they were going to be bound by it so they do regard themselves as bound by it.
“So I think there is little doubt that we’re going to leave. It would require an extraordinary turn of events I think to stop. Minimising the damage, getting as normal a relationship as possible is the best we can really do.”
On the prospect of another referendum on any deal agreed with the EU, the veteran MP said: “I don’t want ever to see another referendum in my lifetime.
“The idea that having put a very complicated question about ‘should Britain be a member of the European Union’ you now put a question saying ‘have a look at this long list of terms that we’ve now negotiated with 27 other states, do you approve of this or not?’ would be folly, it would be bizarre.”
He added: “I do think that no deal is very unlikely.
“There’s nobody on either side of the channel, no sensible person engaged in government or politics or business who thinks that no deal is somehow desirable. It would be totally disruptive.”
Mr Clarke’s comments come as David Davis prepares to travel to Paris on Monday for Brexit talks days after French President Emmanuel Macron suggested Britain would need to up its divorce payment offer to unlock trade negotiations.
The Brexit Secretary will have dinner with French foreign minister Jean-Yves Le Drian in the UK’s latest attempt to jump-start withdrawal talks with the European Union.
France is seen to be taking one of the EU’s most hardline views on the exit bill after Mr Macron suggested at this week’s European Council that it could top 40 billion euro (£36 billion).
The president said that earlier indications the UK could offer around 20 billion euro (£18 billion) to ensure its EU partners were not left out of pocket due to Brexit did not go halfway to what was required.