How it's worked out
A normal year has 365 days: 52 full weeks plus one extra day. That gives 260 weekdays, plus one more if the extra day is a weekday. Leap years can have 262.
Subtract the bank holidays that fall on weekdays – 8 in England and Wales, 9 in Scotland and 10 in Northern Ireland in a normal year – and you get the number of working days. Substitute days mean bank holidays almost always land on weekdays.
After annual leave
Full-time workers are entitled to at least 28 days' paid leave, which can include bank holidays. So a full-time employee on the legal minimum actually works around 232 or 233 days a year.