In general, fancy dress outfits are not appropriate for regular theatre performances in London. While they might be fun for costume parties or specific themed events, wearing a fancy dress outfit to the theatre can be disruptive to other patrons and disrespectful to the performers.
However, there are exceptions to this rule. Some interactive or immersive theatre experiences, such as murder mystery dinners or shows with audience participation, may encourage or require attendees to wear costumes. Always check the specific guidelines for the show you plan to attend.