No. Well, there's not one at the Royal Opera House for ballet there. I'm a regular, and once made a special effort for a gala performance. There were only about six people, including myself. wearing 'black tie' and most didn't have any tie, black or otherwise! The modern way is the bohemian way amongst us 'arty types'.BUT the women make an effort and dress in proper dresses. No jeans for them ! And the effect is incongruous.Casual men with smart women !
It may be that the provinces are a tiny bit less casual, but go how you feel comfortable.They'll think you're a knowing, arty Londoner.The dressed-up ones (if any) are the ones who obviously don't go to such events ! Anyway, Nutcracker is a family ballet, for everyone and all ages, particularly the chidren, so it really never has demanded more formality than,say, a panto would