In an unusual outburst Mr Clarke says he thinks the Kremlin will simply stop taking the PM's calls as Britain will lose its place in the world.
And the 76-year-old, who has been a pro-European since taking up his seat in 1970, says he wants to keep the "free trade" with the EU and snub the rest of the world comparing offers from the US, Australia and India to Alice in Wonderland.
There are currently 700,000 pages of EU red tape connected to rules and regulations governing the single market which Britain has to adhere to.
Ken Clarke like Nick Clegg cannot see past the 'single market'
I basically think you cannot put new trading barriers between yourself and the giant free trade area upon which we have been dependent for the past 30 years without making yourself poorer
But Mr Clarke, the MP for the East Midlands constituency of Rushcliffe, south of Nottingham, says he doesn't want to see change because he claims the country has been "dependent [on the EU] for the past 30 years".
Seemingly unaware of current trade deficits he also says he thinks the country should continue to pay up to £20bn-a-year for the priviledge of its depenency.
Known for his sartorial like of Hush Puppies, Mr Clarke was the only Conservative to vote against Theresa May's government second reading of her Brexit bill.
Mr Putin was in Hungary meeting new PM Viktor Orban last week
Now, after becoming a darling of the Labour opposition benches for refusing to vote with his party or change his mind, he's enjoying the limelight, he says.
Mr Clarke told the Guardian: "All political careers are a rollercoaster.
“It is nice to have a week with some fans.
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"It’s quite obvious that some of the 16 million [who voted to remain] were much bucked by the fact that somebody was still being as obdurate as I was and refusing to see why on earth they should all be abandoned.
"Actually, I think the 16 million were right.”
Mr Clarke and Mr Clegg are both supporters of the unaudited undemocratic EU
When quizzed on foreign policy, the former Chancellor, who lost the chief finance job in 1997 after Tony Blair's election, said Mrs May should spare a thought for Russian relations.
He said: "I don’t think President Putin will bother to pick up the phone to Theresa May if he’s busy. We don’t matter so much any more".
Mr Clarke also said he voted to keep the majority of his constituents happy.
He added: "Fifty eight percent of my constituents voted to remain and you want me to tell them to clear off?'
Theresa May will not be able to get Putin on the phone post Brexit says Clarke
Maverick MP Mr Clarke is also opposed to the Prime Minister's desire to enter into global free trade agreements.
He told the newspaper that he thinks the UK is putting up barriers despite the majority voting for an exit.
He also failed to accept that any barriers will be implemented by the EU who have indicated that they want to punish Britain for leaving the unaudited undemocratic body which governs UK law.
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Mr Clarke added: “I basically think you cannot put new trading barriers between yourself and the giant free trade area upon which we have been dependent for the past 30 years without making yourself poorer.
“I don’t want to fall into the [trap] of wandering around, positively welcoming gloom and disaster, so as to be able to say: ‘I told you so.’
"But I actually do think it will make us poorer. It could be a historic disaster.”
“If it turns out to be at some enormous cost and it brings an end to international investment in quite a lot of sectors of the economy, then of course it could be a disaster.”