Less clear where it comes from. It's said to have been first used in early 21st century online sports forums, so not something that goes back to the beginning of time.
'Cock' means 'prick' and a 'cock-up' means serious idiotic mistake or messing things up completely (Brexit would be a good example of a cock-up)! But in the past, 'cock' was also sometimes used to mean 'champion' - like a strutting rooster, I suppose. The boy who could beat everyone else in the school - at sports, or just by beating them up in fights! - was sometimes called 'cock of the school'; and people who thought too much of themselves were often described as 'cocky'. Less used nowadays in that way.
So I think 'cock' in 'cockwomble' combines both meanings as in 'champion prick'!
The womble part? That's more puzzling. The Wombles were imaginary furry creatures who lived on Wimbledon Common in a set of children's books and then a TV series in the 1970s. But, as a Wimbledon child of the 1970s myself, I would like to confirm that the Wombles were very lovable characters, and indeed early heroes of recycling: they would pick up litter and recycle it for good purposes in their underground homes. The theme song of the TV programme, which became a popular hit song in its own right, began:
'Underground, overground, wombling free,
The Wombles of Wimbledon Common are we,
Making good use of the things that we find,
Things that the everyday folks leave behind!
So I don't see why Wombles would have a bad connotation; but maybe there is some other derivation.
Anyway it's a satisfying insult. Became better known and better used after the Scots used it to describe The Unspeakable, after he visited Scotland and congratulated them on Brexit (which Scotland had voted overwhelmingly against, so it's basically the equivalent of going to California and congratulating the locals on the election of The Unspeakable).
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