I don't think any UK banks are friendly to crypto sellers regardless of whether you are using a business or personal bank account. It's too high risk for them, closing your account is more profitable than the hassle/cost of AML and KYC checks it will bring later on.

Why don't you buy from one of those big traders then you will know which bank account they are using? My guess is they switch between a few accounts and/or are using accounts which can hide the trades ie they have businesses with a lot of deposits from non cryptocurrency sales.

Not many banks use Faster Payment so it's not a long list anyway.