The irony of that sketch is Cleese has turned into one of them...
Seriously? Have you seen him in interview recently, and seen something I haven't? Every thing I've seen from the man indicates that while he is quite active in political process, he's also pretty progressive in his views.
He lives in the Carribean, and tweets that London "is not really an English city any more"
https://www.bbc.co.uk/news/entertainment-arts-48451384
Ummm... yeah. And if you read the article you linked to, it is pretty obvious that his actual views are still as progressive as ever. Its the tabloid media trying to make him sound like a bigoted arse using moronic sound-byte manipulation, as is their stock in trade.
The full interview is here: https://www.bbc.co.uk/programmes/p06df6qd
If you listen to the guy, he says he's spent enough of his life fighting the good fight and is moving just to get away from the right-wing nuttery. He chose Nevis because they're A) Generally well-educated in the traditional English style and 2) he's tired of the constant BS level of Western tabloid press, which in his opinion, ALL press is severely right-wing slanted and full of BS. He likes Nevis because "their press is very tiny", not necessarily any less full of it.
It appears to me that he's leaving Britain because of the BREXIT circus, not that he's necessarily a BREXITer. His complaint above was that there simply was no discussion between the left and the right on BREXIT; it was all knee-jerk sensationalism on both sides of what he correctly characterized as "it's terribly complicated..." I can generally agree with all of these attitudes; there's a reason I'm moving my children to Canada.
Of course, as is the case over here, the one thing politics cannot stand up to is the light of day; ANY reasoned consideration of actual facts and outcomes vs the greater good will always be drowned out by whomever can lie the loudest with the biggest megaphone in a 10-second soundbyte.
[EDIT]
While I generally believe that BREXIT was the second biggest sham putup fleece job of the millenium, that is also predicated upon a very limited understanding of all the ramifications. I know Cleese to be frightfully intelligent and a shameless intellectual with a greater-than-average understanding of British politics. I can see him weighing a lot more stuff than I really know about & deciding in favor of BREXIT as cauterizing a wound; really painful but needing to be done to save the patient. Especially as he is generally very "traditional Brit" in his sensibilities.
[/EDIT]
I think you've bought the PR a bit there.
He's fed up with the press because literally every single paper here, not just the tabloids, keeps digging up the gigantic turds he keeps laying everywhere such as acting as a paid mouthpiece for the lib dem/conservative coalition, then strangely disappearing off the planet when this turned sour leaving our universities in ruins with tuition fees hiked at £9k a year. Oh and buggering off to Monaco, a tax haven, to avoid a hefty unpaid tax bill after his ex wife ended up with a large alimony payment.
He naively blunders around using his celebrity credentials to mouth off on politics only leverage speaking appointments, following popular ideologies to their destruction quickly running away, throwing all his cash in funds and hooky tax dodge schemes.
The ONLY reason he buggered off to Nevis is the EU dropped it form the tax haven black list in 2018 conveniently just before he made this decision. It's now on the grey list, which is a sort of "we promise to get our shit in order but we're still a tax haven tee hee".
The reason he decided to support leave and fuck off to Nevis was the same reason our politicians do, which is increasing financial regulation (boo hoo less rolexes). The main impending thing which might even possibly be the entire reason for Brexit is the introduction of ATAD:
https://ec.europa.eu/taxation_customs/business/company-tax/anti-tax-avoidance-package/anti-tax-avoidance-directive_enBear in mind taxation in EU is higher but we basically get things like healthcare for it. Some people resent paying that, probably like Cleese as he's been seen going in and out of a BMI private hospital a few times here...
There's another suitably British person with a higher profile that might be of interest if you wish to read up on well spoken British intelligent sorts of people: Jacob Rees-Mogg ...