Hi, Sofia,
Welcome to the forum. I walked the Camino de Madrid in May 2012. I met two pilgrims in Manzanares and we walked together till Simancas, where I wanted to turn off to visit Valladolid for a day. From there on, I met no other pilgrim. There seem to be more forum members planning the Madrid, and a number who have walked it recently, but if you search through the Camino de Madrid posts I think you will see that most of them, even the ones who walked more recently than I, had a similar experience with solitude.
It is an extremely well marked camino, great pilgrim infrastructure, interesting places to visit. If you can speak Spanish, you will be fine and will easily find company in the cafes and bars. People in these towns love to speak with pilgrims, because we are such a rarity on the Camino de Madrid.
I've also walked the Vdlp in May and you will certainly find more pilgrims there. It is a glorious time to walk, when I started in early May, I always had company at night, and sometimes during the day would walk with others if the mood was right, but I do love walking alone!
No doubt that if you want to be assured of more company, the Vdlp is going to be a safer bet. Buen camino, Laurie