Absolutely recommend Soccer Stars Academy run by the fabulous Denzil. He runs several sessions for different ages from 3 upwards on Saturday mornings (each is 45ish mins long, think he does sessions at 10am, 11am and 12pm) on peckham rye in between the cafe and the east side of peckham rye road. my daughter went when she was younger (before deciding it was her thing) and my 4 year old still goes and absolutely loves it. Denzil (and his team) are great with motivating the kids, definitely our favourite extra curricula activity! you can contact him on +44 7522 425931
Our son goes to (and really enjoys) footballmagiccoaching.co.uk which is £7 a session (£42 per half term). There is a reception class on Wednesdays after school in Peckham, there may be weekend sessions too.
I can also recommend Athenlay - it is very welcoming for boys and girls who want to play football from a young age, and also has the option to progress into a team and play matches in the Selkent League.