Yes, road racing and club riding are nearly synonomous. Makes what is a pretty tough form of cycle racing a *tad* more enjoyable! Both Dulwich Paragon and Addiscombe CC are well-known and supported South London bike clubs.

But as andyp says above, the racing itself is tough as the pace is high. If you can't get round Richmond Park in sub-19 mins I would do a bit more training, or start racing at Herne Hill track first - is a lot more beginner-friendly.