This is why i would never join "all british". The site has really good reviews and Jan seems like an excellent rep but i'm the same as the op, i would never go through sow with any casino, i would never show bank statements etc. I totally understand they are following ukgc responsible gambling and anti money laundering regs but that information is private and i'd never provide it and just close my account with said casino!
Casumo wanted all this sow after me depositing over £13,000 lol, i just closed my account, luckily for me there was no withdrawal pending surprisingly! I like the way white hat sites tackle this issue 2bh, they put a £500 loss limit on your account across all their sites and the only way you can raise that amount is by completing sow, so if you don't want to do sow then you can just stick to a £500 monthly limit, which is fine by me ;-) Also sites like gamesys (jackpotjoy, virgin games etc) never even ask for id, nevermind sow lol.
I really think though the op should get their withdrawal from all british after closing account though, if the casino doesn't suspect money laundering and the player has closed account/ended relationship with said casino then they should definitely get paid the withdrawal in my opinion!!!
I'm similar to you in the way you use your banks for gambling.
I've just sent All British the bank statements that relate to the debit card used, but I've blanked out every transaction that's not to or from them and also shown all of my payments to my account from my business account. That's what I've declared as my source of wealth and that should hopefully get my withdrawal sorted.