Some myths here.
I have worked as a mortgage underwriter (residential and BTL) since 2006 for various lenders (I wont say who) but....
1. Those credit score things are completely meaningless to mortgage providers - mortgage providers have their own internal scoring system which is based on a vast matrix of information, every lender is different and it is all based on statistics and risk indicators, its actually a very complex scoring system.
2. Voters roll history is by far the most important thing you can have, if your voters roll history matches your address history, thats half of the job done right there
3. Unsecured debts (residential specifically) can affect your applicaiton, all lenders now have to do affordability calculations since MMR (mortgage market review) kicked in, somewhere around 2014 (dont quote me on that!) but (although slightly simplified for this forum) they basically look at your income vs your outgoings. Most of the outgoings are based on ONS statistics for someones age etc, otherwise they would need to go through every single trasnactions on your bank statements to see how much you spend on food, travel, closthes, bills etc etc (although there are apparently some lenders that do this lol!) the vast majority dont. However, debts are debts, loan outgoings/credit cards are what they are and will be deducted. Most lenders also specifically look at things like childcare costs, ground rent and service charges.
4. The old credit card will improve my score debate - actually yes it will, but it doesnt make that much difference. But lets look at some of the above comments - the hard search will marginally affect your credit score, but I would say the benefits outweigh that, most credit providers a single search, even recent will not affect the lending at all. Its only when you start to see 6, 7, 15 searches in teh last few months that then becomes a concern. If you have a credit card that you repay every month (so you dont pay interest) it wont cost you anything, and will improve your traceability, also particularly if you keep phoning them every month to get your limit increased, having a high limit/low balance is a positive, because it shows, despit the fact you have the available credit, you are not using it, and that shows good financial stability.
5. loans, car finance any other debt really only hurts you, and never ever (ever) take out a payday loan of any form
6. Despite what you might think, most mortgage applications are quite closely looked at by a real human, like me, and you wouldnt believe the amount of personal informaiton we can get about your and your property. Provided you have reasonable explanations for anything unusual, its normally not a problem, but never lie, believe me they will know.