If your going down the LTD route then you can buy a LTD Co off the shelf with a Bank Accounts included, ie ABC LTD T/A your Name of Choice, other wise get an Accountant to do it ir all for you and probably pay a bit more!
Other wise do it all yourself, but be prepared, as its no longer easy with the big High Street Banks, which is what you need really if your serious about your Business.
Be prepared for proposed Business Plans, Market Research and Forecasts to open a Business Account, other wise you will just get rejected, also Credit References must be good for the Directors even for a LTD Company.
One one forward could be a simple Telephone Banking Business Account, which you can update over the Net to on line Banking within days of acceptance, giving you all the benefits of simple banking, payments in and out free of charge, Debit Card, Cheque Book, etc all for around £10 a month or free for the first 12 months, NatWest are good for this, takes about a 10 min Telephone Interview to set up and generally gets accepted on the same day.