There are a few field trials in late July/August/September (on rabbits) but the bulk of trials are held from October when the pheasant season starts. Novice trials will be held up until the season finishes on 1st February, Opens finish before the Championships in January. Spectators are allowed at most trials at the discretion of the secretary/organiser so you really need to contact them in advance to check arrangements; I would not take a pet dog. There are scurries and working tests throughout the spring and summer at most game fairs and also organised by various gundog clubs. Most scurries are 'have a go' and can be entered by anyone with any breed of dog, the club tests are often divided by breed or breed type (AV spaniel/retriever/HPR) and have to be entered in advance. Both scurries and tests use dummies as opposed to live game so are not entirely authentic but are fun nonetheless.
It would be extremely difficult if not impossible for a show Cocker to compete in field trials (and also most working Cockers). Trialling dogs need massive amounts of natural drive and speed as well as intensive training, they're not your average pet dog - I have one. My 5 year old bitch is a Field Trial Champion, she was handled by a professional trainer, and she's a totally different kettle of fish to even my 'normal' working dog. She's wonderful, but not an easy dog to live with. Trials are elite competitions, highly competitive, and relatively very few dogs are capable of succeeding at that level. They're amazing to watch, if you look at the websites of the various KC affiliated gundog clubs and/or the KC field trials diary later in the year you'll almost certainly find a trial being held somewhere near you in the autumn/winter.