Is there a bank supported by quickfile to open a free bank account for a new Ltd. company?

I believe it was Yorkshire Bank (which is now part of RBS).

I applied as a sole trader. I would imagine applying as a limited company should be easier, certainly when I have opened accounts at suppliers providing references as a registered company has been easier IME.

I wasn’t recommending using a personal account for business use. As you quite rightly say, a lot of banks frown upon this practice.