You are legally entitled to a minimum of 20 days off a year (assuming you work full time hours - if you work less hours, the number of days you are entitled to is pro-rata'd.
With the exception of banks, there is no law that stops companies operating on bank holidays. Companies that do not open are not legally obliged to pay their staff for that day off although if they want to, they can insist that the day off comes from their annual holiday entitlement. This should be detailed in the contract. Where the contract says nothing, look at what has happened previously.
So to summarise, there is no legal requirement in this situation with the exception that if you work, you should be paid for doing so. However, do check your contract/the company handbook/the experiences of people who have worked there for a long period of time to see what the Company tends to do in that situation.