In reply to Chris Mifsud:
You can top rope solo chalk (avoid any that has flint bands as it is like a row of knives). There are some outcrops on the coast east of Margate, on that whole coast from Margate to Beachy Head even many leadable documented routes if you are clinically insane. Either hard chalk as a rock climb or soft chalk as "ice" climbing. Not sport climbing though.
Less insane, you have sandstone bouldering and top rope climbing to your west, Google "Southern Sandstone" to learn more. Again this isn't sport climbing but it can keep your climbing muscles working. If you think of Southern Sandstone not as something serious but as just a laugh, then you can have a really good laugh, enjoyable and definitely worthwhile but in it's own way!
Obviously in addition to the above non sport climbing you can always go into a bouldering wall/gym and have a chat with the people who work there, they can advise a local club. Enjoy!!