This is the process I had to follow back in 2005, I don't think it's changed much
1) Choose a bank - several to choose from in UK. Most offer free-banking for a year/18 months. Alliance & Leicester, plus Abbey - who are now owned by Santander - currently boast:
- FREE and UNLIMITED day to day banking*
Not offered by any other bank
- Market-leading cash deal
FREE cash deposits up to £3,000 per month, then just 50p per £100 deposited
- Unrivalled access and convenience
Bank online, via your mobile, over the phone or at any branch or Post Office®
- Competitive interest rate
Earn 0.25% AER (variable), 0.25% gross (variable) on your whole balance
*"FREE and UNLIMITED day-to-day banking" excludes CHAPS payments, changegiving and other non-standard charges. Interest is calculated daily and applied monthly.
Whereas HSBC offer free 18 months banking.
2) Get business bank application form - paper or on-line.
3) Most application forms will require: Name & address of Limited Company, Company Registration Number; when was business established (month/year); estimated annual bankable turnover; how long have you been with current bankers (personal or existing commercial bank); brief description of your business; total number of directors; a veiled question if you are a money launderer

New incorporated companies (less than 18 months old) may need to provide:
(a) a copy of Co House doc 288a - Appointment of director or secretary - for each director or secretary,
(b) a copy of Co House doc 88(2) - return of Allotment of Shares, or
A letter of confirmation of the shareholders from your accountants or solicitor.
Next: Account Holders personal details: name, DOB, address (with post code, and how long you have lived there), phone number. If it's under 3 years you come under more scrutiny! All these details are required for each director and Co Secretary, or @ least 2 directors.
(c) Sample signatures of each proposed Account Holder.
(d) One of the usual selection of CERTIFIED copies of ID docs: current valid SIGNED passport, current full UK driving licence, etc;
plus One of the selection of CERTIFIED copies of proof of address: a current utility bill, water bill, mortgage statement, etc.
(e) These items may be required: Certificate of Incorporation(of Ltd Co), Memorandum & Articles of Association, and a Statutory Statement certified by an auditor.
............... I think that's enough for now, to convince anyone not to go Ltd Company "on a whim" 