I'm sure I posted similar before but please do bear in mind that your credit score isn't really all that important when it comes to actual lending. It's not a rating of your "credit worthiness" at all and, in most cases, lenders don't even see your "score".
The subject of the UK credit system is a complex and painful one as decision making is primarily based on what's called CAIS (Credit Account Information Sharing) data that details all of your accounts, usage, credit solvency etc over a rolling 6 year period. Most lenders have an affordability criteria that includes a "stretch payment" (essentially what would happen if interest rates changed - and yes I know you said it was 0% but that matters not a jot in the way that most lenders review).
Secondary to all of this is that there is no definition of what "good credit worthiness" actually looks like, there's no defined standards and all lenders work on the basic premise that they are under no obligation to lend and therefore can set their own criteria (I've worked in 5 different retail credit businesses and all have different thresholds and tolerances). This basically means that they don't even need to give you a reason and this is how they can just direct you to the reference agencies (passing the buck) as the reference agencies can't really tell you why a lender said no as they are not the lender.
If you have a credit card with more than 60% utilisation of balance for example, this can affect decisions to lend, if you only make minimum payments to short term lending accounts (which includes credit cards) then this will impact. If you have opened new credit or banking facilities in the last 12 months. If you have newly erratic or heavy usage of a bank account (even if the balance in the account is healthy). Voter role omission is one of the biggest problems for lenders. Essentially any activity that makes a lender nervous can trigger it.
Now, with all that said, an outright decline (rather than a referral) is a definite indicator that your CAIS data has something in it that the lending criteria isn't liking.
Also, on the subject of people at your address, these should only affect you if, in your CAIS data, they are registered as a financial connection. And that usually means joint account, joint lending or being guarantor for someone. Simply living at the same address is not considered a financial connection in majority of cases. This used to be the case (as well as people previously living at the address) but changed a good while ago.
There's also no such thing as a blacklist or any other list that may have existed decades ago before computerisation of data took place.