Here is the web dirrection of the "Federación de Tenis Mesa" of Spain.
www.rfetm.com
You can find a list with all federations, clubs and the leagues. (Go: links - federaciones) Go to the "Federación Madrileña" and than look at clubs. I do not know the clubs because I´m in Valencia.
Leagues are:
National:
- Superdivisión
- Division de Honor
-1ª Nacional
-2ª Nacional
Territorial (Comunidad Madrid)
-3ª Nacional
-1 Comunidad de Madrid
-2 Comunidad de Madrid
....
If you want to play territorial leagues you have to inscribe at least beginnig of September (no idea for national) and you will need a certification from your old club that you a "free" for playing.
I think there is a "forum" where you can ask too.
Regards Wolfgang