Bank/BS for 'existing customer' deals

Porcupine

I'm currently working down the list of banks and building societies offering regular savings accounts, with the aim of opening a few. Quite a number are institutions I've not dealt with before, especially various building societies, which causes me to wonder... are there any which are better at offering 'existing customer' mortgage deals, so that by having an account I could get access to mortgages which I wouldn't as a random off the street? I don't currently have a mortgage.

Or alternatively, is it like car insurance where you get a better deal as a new customer because they want to attract new business? In which case, I'd be closing off my options by wasting my 'new customer' state for a mere few pounds interest.

amnblog

Why are you seeking to open numerous accounts?

Porcupine

Because that's the best way to do savings these days. Multiple current accounts pinging money about and, once you've run out of those, regular savers. Which always have some limit like £300 per month, so you might need several to put away a larger sum.