Matt,
I’ve been a member of British Cycling for a number of years and sadly there is no such thing as reduced membership for club members. (And sadly it used to be a lot cheaper a couple of years ago).
They do promotions to encourage new membership such as one ending this week for a free training journal (use code TRAIN14) on check out.
The main thing to consider are the benefits against the cost of £32. (mainly the public liability, legal cover etc). I’ve also taken advantage of free entry to sportives, priority tickets to Olympics/world cup events etc) as well as money off at various shops.