I have moved a great deal both here and abroad and would always recommend the library as one of my first places to visit. They normally have the latest up to date contact address for many different kinds of associations and clubs. So you can look for the things that interest you there. If you swim, the local swimming pool is also a great place as you have an activity which allows you to get to know other swimmers over time and you may find people on your wavelength there.!
To think that London, or anywhere else for that matter, does not belong to any one demographic