Two main routes - college or on the job training or a bit of both. On the job training hard to finds as most employers want some experience so college is a good place to start -to see if it really is your thing first and the City & Guilds Level 2 qualification is the place to start.
Best place for some background info is the Society of Floristry website www.societyoffloristy.org
As for training in your area best googling for floristry courses south london. There are loads of private courses but colleges generally cheaper.