You would need to speak to your bank but normal practice is to move your account as when you enter an IVA chances are your Creditor (Bank) will attempt to take the payments out of your account.
Natwest and Co-op come highly recommended. You have a Solo debit card with Natwest and Visa Electron with the Co-op
If you're not in an IVA yet you may be able to open a full bank account with a bank who aren't one of your creditors. It really depends on your credit rating - have you already missed payments to your creditors? If you have it will be difficult to open a full account.
All debts must be included in an IVA even if the debt is relatively modest in comparison to the total. As Skippy says, try other banks immediately as you are not currently in an IVA and your credit file may not be badly impaired.
Only if the debt or overdraft was cleared and any facility cancelled could you continue to operate with your existing bank.