I know one amazing class called Latino Bambino - basically it is baby salsa.
In the Vitality centre on Fridays .You have to try .

If you are willing to travel just a bit more, there is a Pilates class in Earlsfield where you can bring your baby.
It is in Prophysiotherapy clinic..very nice setting and lovely people.

Does anyone know of fitness classes that you can bring baby along to in Clapham or Balham? I have done buggyfit in the past, but tried to find a mum and baby Zumba or yoga class but the ones I knew of when I had my first son are no longer run. Any recommendations greatly appreciated!