UK bank holidays differ by nation
England and Wales have 8 bank holidays a year. Scotland has 9, including 2 January and St Andrew's Day, but no Easter Monday, and its summer bank holiday is in early August. Northern Ireland adds St Patrick's Day and the Battle of the Boyne. When a bank holiday falls at a weekend, a substitute day is given, usually the next Monday. Pick your nation in the sentence above and the right days are skipped.
Notice periods, invoices and deadlines
Many contracts say "10 working days" or "within 5 working days". Use Add or subtract days: the day you start from is not counted, so the first working day after it is day 1. Court time limits in England and Wales follow their own rules (for example "clear days" under the Civil Procedure Rules), so check the rule for your case.
See the UK bank holiday lists.