If you're interested in the competitive side of cycling and want to know how to get involved then read on.
Firstly, there are two sorts of time trial events: Club events and Open events. Club events are open to anyone, even if you're not a member of a cycling club - because you can become a temporary member of Charlotteville for that evening. Generally, there is no need to enter in advance for club events, you can just turn up on the day to sign on and ride. Entry fees are currently £2 for Charlotteville CC members (first or second claim) and £3 for non-members. Courses and events are described here.
Then if you want to step up from there you need to look at Open events (which as they suggest are open to, and organised by, all clubs). When I say they are open to all, they are open to riders from all CTT affiliated clubs (except where there are restrictions such as needing to be a Veteran/Lady/Tandem/Trike etc.) Being a member of Charlotteville CC means that you can tick that particular box. Entry details for each race can be found in the CTT handbook which contains all open event listings. The races take place up and down the country on all weekends (and many weekdays) during the year. You have to enter the event about 2 weeks in advance and these days most of the events are managed using the CTT online entry system. Races are usually about £6-£8. Entries are based on previous times and for most races the field is selected on the fastest riders. On the day of the event you need to go to the race HQ and sign on (where you also get your number). You must either wear club kit or plain coloured kit. You are not allowed to wear either trade team kit (unless you happen to ride for that team) or kit with any advertising that is not an official sponsor of your club. Make sure you get to the start about 5mins before your start time and then its pretty much as you would expect for the rest of the race. Results are usually posted on a board in the HQ and in return for bringing back your number you usually get a free cup of tea. Ypou also need to 'sign out' which is something that has been introduced in recent years as part of the CTT anti-doping controls management approach (as any riders required for testing are notified via the sign-out process). There is also a section on the CTT website covering a 'Beginners Guide to Time Trialling' so go look at that too. Enjoy your ride!
The British Cycling website contains a number of articles about how to get started with road racing and other cycling disciplines. The key thing is that, in general, you need to have British Cycling membership (and you can get discounted membership for the first year either through the club, contact the membership secretary, or just by doing a bit of 'Googling') and a racing licence to take part although there are exceptions these days (Go Ride events) where you can try out road racing without having either British Cycling membership or a license. The Surrey Cycle Racing League (or Surrey League) is a local organisation that aims to provide a full years worth of racing across all categories or riders in the local area and as an affiliated club our members are able to join the Surrey League and ride in their events. As a result of this we are obliged to organise events on behalf of the Surrey League and therefore members are also expected to assist with this organisation. In recent years the Surrey League have also required that all riders new to road racing complete a course (covering basic racing skills and safety aspects) in order to qualify to race in their events.
Not competitive events but they are very popular these days. You don't have to be a member of a cycling club to enter these events but its nice to ride with other club mates. To find lists of these rides go to either the British Cycling website or the Cyclosport.org website.
Before sportives came along there was also branch of the sport called Audax riding which are long distance cycling events using a system of timed checkpoints. For more details about Audax events (which are usually a lot cheaper than sportives and some of them can be ridden at any time!) go to the Audax UK website.