This is an interesting thread for a crypto gambling forum I'd say.
Most operators that are popular here hold only the Curacao eGaming license and that practically makes them illegal websites for British customers. Basically, Brits should gamble at UKGC casinos only and most operators here don't have that one.
I guess everything depends on how you define 'illegal'. If a website has good reputation but accepts UK players even though that's not allowed, is it an illegal one in your eyes? Because it's definitely not 100% legit but it's also a trusted brand with lots of positive reviews. So, I think that there's a bit of a grey area.
I know for a fact that many UK players play at international and offshore gambling sites. Why? The reasons are plenty. They want to escape Gamstop (no smart btw if you have a gambling problem), they want to make credit card payments (banned in the UK since April 2020), they want more freedom, etc. In that regard, I'd agree with the OP thesis that the black market thrives in Britain. But, I wouldn't say that it's 100% black, maybe grey in most instances.
Like, these operators do perform KYC checks and follow some rules. They're just not as strict as the ones approved by the UKGC. Also, some of them may be scam operators who just want to steal your cash, avoid approving withdrawals, and stuff like that.