I’d second the recommendation for Believe in Magic dog training - our dog loves the advanced class
Sadly London is not particularly blessed with agility classes ... there’s one in Ham, near Richmond
http://www.capablecanines2002.com/
Otherwise you’re looking at further out - google found this one in Chessington (I have no idea what it’s like though)
https://citypawsclub.co.uk/training/agility/
And Scrambles agility has a good reputation
https://www.scramblesdts.com/agility/ but is a pain to get to and most of their classes are in the early evening just when traffic is at its worst
Good luck in finding somewhere - and if you do find somewhere closer let us know