In most courts,from the Old Bailey(Criminal) & The Royal Courts Of JusticeCivil,(now The Sumpreme Court) down to a Magistrates Court,there is usually a Public Gallery or Section.
If you know which court you wish to attend,give them a ring and they will advise you.
Anybody over 14 can attend any of the courts of law and sit in the public gallery.
There are a few exceptions. These generally centre around youth proceedings (that is where the defendant is under 18). Youth courts are generally closed to the public.