There is no statutory right to holiday, with or without pay, on bank or public holidays.
That being said many workers are entitled either to paid leave or to overtime rates of pay on bank and public holidays under the terms of their employment contracts. There may be express contract provisions or there may be implied terms such as customary arrangements which may amount to implied terms of contract (see notes at Implied terms in employment contracts ). If express contract terms are ambiguous the courts will look to see how in fact the contract has been operated in practice (see for example Blows & ors v Dunlop Tyre Co (CA) 2001 , Court of Appeal on 18th June 2001).
In 2005 the government announced plans to provide that bank holidays would cease to be counted against the statutory entitlement to 4 weeks paid holiday. This proposal was dropped. Instead statutory annual holiday entitlement was increased from 20 working days to 28 working days for full timers, pro rata for part timers, phased in from October 2007 to April 2009 (see notes at Holidays/2007 changes ). The 28 days annual holiday entitlement is inclusive of any bank and public holidays.
The Christmas Trading Act 2004 prohibits any large shop from opening on Christmas Day in England and Wales. It means that many a shop worker will in practice become entitled to Christmas Day off, regardless of whether it is on a Sunday or any other day (see Acts of Parliament etc/Christmas Day Trading Act 2004 ).
The DirectGov website provides a list of statutory bank and public holidays for England, Scotland Wales and Northern Ireland, 2010-2012 inclusive. There is also a general government website re Bank Holidays.
See also notes at Working Time Regulations/holidays and for international comparisons see Holidays/a general note (professional versions only)