Could the Bank close my account?

The Financial Services Authority includes in its Principles for Businesses: "A firm must pay due regard to the interests of its customers and treat them fairly". You, like any other customer, are entitled to make a complaint if you feel you are being treated unfairly. You should not be prevented from making a legitimate complaint by the threat of having your account closed; nor is it fair or reasonable of the bank to respond to your complaint about charges by closing your account. Any bank which appears to have used the closure of the account as a retaliatory or punitive measure would certainly be viewed very dimly by both the Financial Services Authority and the Financial Ombudsman Service.

As a general principal banks are entitled to decide whether or not to provide banking services to any particular customer. That is a matter for their own discretion.