No - open 10s have to be entered about 2 weeks before using an entry form found on the CTT site (entries close the Tuesday week before the event if on a weekend - so if an entry were to close in 2 days the event won't be until the weekend of 3rd/4th July).
You can turn up at club 10s and sign on about half an hour before the event is due to start. Almost all clubs are welcoming at club time trials, but if you aren't already a member of a club you may be asked to join one after a couple of rides.
You're actually pretty fortunate with your location - you have a choice of 3 districts within easy reach: Central (A), Midland (K), South East Midlands (N). The Midlands has a brilliant website which will tell you when and where all club and open time trials are. For the others it is a case of finding club websites and then looking at their event list.