In many cases, yes they can.
Some employers add the eight bank and public holidays, including Christmas Day, on top of the minimum leave entitlement (which is 5.6 weeks/28 days per year for those working five days a week). You should consult your contract of employment to establish the exact position in your company.
On the other hand, some employers may actually include bank holidays and public holidays in the minimum leave entitlement. This Scrooge-like approach may be mean, but it's not illegal unless your contract of employment says otherwise, or you are being treated differently for an unlawful reason (e.g. because you work part-time).