Dunno whether it's a particularly British thing, but there are generally two components to a wedding - the ceremony and the reception. The former involves the vows and "I do" etc and is often followed by a formal dinner. The reception is basically some variety of music, booze and buffet, taking place later in the evening.
As formal dinners are expensive, the close family and friends are often the only ones invited to the ceremony, whilst workmates etc are invited to attend the cheaper reception, or 'night do', so as many people as possible can share some part of the day without financially ruining the bride's father.
EDIT: oh, and of course, who you invite to the ceremony and who you invite to the reception is a social minefield. A badly considered omission from the ceremony and friendships can be destroyed, families torn asunder, Aunt Doris may amend her will. Following this up with an invitation to the 'night do' is simply kicking them when they're down. This may help explain the verbal quotes clearly heard around the word 'night do' in this episode, highlighting the withering putdown the person has been subject to.
If someone goes to a 'work do', it's a night out with people from their employ. Just to confuse you, a 'do' is also another way of saying hair style and a 'to do' is an argument or fight.
