Just googled Cycling time trials and it says ...
Entering Events
Whatever type of time trial you are entering, club or open, you must be a member of a club that is affiliated to Cycling Time Trials. Being a BCF or CTC member does not generally qualify you to ride time trials unless your BCF Division or CTC District Association is affiliated to CTT.
However, if you were to turn up at one of evening 10's, you can join our club on the night and we have a policy of "first year is free".
I'm sure other clubs would have similar arrangements - they are unlikely to turn away a prospective new member.