There are a few company formation agents that as part of an added fee , they guarantee you a business bank account.
But last time i set up a company, I simply used my accountants to do it - they took care of everything, and sent me stuff to sign and send back to them. Idiot proof.
They also allow you to use their company address as your registered address, so all the dreaded returns go straight to them and they fill in the stuff. You of course can in turn then put this address on your whois, so it has the benefit of privacy, without the drawbacks
For the annual returns they charge low £xx a year, and for the initial company setup, I think they charged me maybe £100ish on top of the regular formation fee.. well worth it IMO.
They also had contacts at Lloyds, so helped push through my application for 2 biz bank accounts, UK sterling and a foreign USD account.
My advice.. yep, you guessed it, use a friendly accountant. If you want me to pass on his details, just PM me.