I'll be 50 in a few months and I'm still skating. I'm still shit too with a repertoire of 0 tricks. Can't even ollie.
I learnt in London in the late 80s so was a 20-something late starter myself. It was a good time to start as skating had yet to re-emerge from the underground of the post-70s craze days. This meant all the skateparks were empty most of the time. Good times..
On the plus side - dude you live in London!!! There are some killer concrete parks form the 70s that still exist as well as all the new ones.
Harrow is a good place to learn - great classic park with very retro features (lethal peanut bowl!)
Kennington - great rectangular mellow bowl in Kennington Park (a quick tube ride from Waterloo/South Bank)
Stockwell - great mellow park right by Brixton Academy (much improved/upgraded since the 80s)
Victoria Park near Bethnal Green/Hackney.
Romford too - if its still there
I'm sure you know these by now. There are loads more.
I also chanced across a new park being built in Folkstone Gardens in Deptford that looked very cool.
I hope you learn new tricks quickly. I stalled early on but I don't care - the buzz of cruising around at high speed grabbing the odd grind on a concrete lip is fine by me and still "does it for me". Sure my son took up skating at 14 and within 2 months was better than me - he takes the piss out of my lack of ability but we still go out together. Going to head out to Hereford again soon -
https://www.youtube.com/watch?v=dP16Hw59Oq0 - great provincial park. Many of the best parks are in weird provincial places. Midsomer Norton anyone? Killer fun park -
http://www.skateboard.com.au/skateparks/england/midsomer-norton-skatepark/.
Dorchester in Dorset too.
I've managed to avoid any injuries in 30 years of skating - but then I know no tricks!! My son has broken the same wrist twice skating in 4 years and shreds. How cool it is to break a bone in pursuit of something you're passionate about. Although the bigger you are the harder you fall - and I'm 49 and tubby.