Yes, I think it might be worth contacting the UKGC about this if 188Bet are still unwilling to pay up after the latest documents you've provided, although there's no guarantee that the UKGC will be prepared to intervene. I've certainly never been asked to provide this sort of information by any online bookmaker prior to a withdrawal request being processed. I've been asked to provide proof of ID, address and (occasionally) a photograph of any card I've used to deposit, but that's all - and I've made withdrawals from a fair number of operators both past and present.
The claim that providing the sort of information 188Bet are requesting somehow proves to them that you are not a money launderer is totally without foundation. I don't see how anyone can prove that they aren't a money launderer by answering questions of this sort, given that this is just one bank account and a person could have any number of others. As long as you have provided clear proof of your ID, address and ownership of any card used to deposit funds into your betting account, then, as I see it, all statutory requirements have been met and anything else requested by the bookmaker is unnecessary.
A lot of players like 188Bet, but I've always had my doubts about them, which is why I've never used them (if you do a search of this forum, you'll see that your case is not unique). I still think you're very likely to get your winnings in the end, but if you're betting in large sums, they my advice would be to avoid 188Bet from now on.