Hello Jean,
There is a huge demand on English teachers here. Native English teachers are pretty much needed at primary schools, language schools and companies. In many cases the English teachers are from countries like Bulgaria, Germany or France.
A friend of mine from Cork, a 41 y.o. lawyer, was an English teacher in Madrid. He went back to Ireland early this year because according to him you cannot expect to get a proper house and raise a family with 10 euros per hour. He used to say "I don't work for peanuts". He said he was going to live in the beautyful and lively city of Dublin because after living in Madrid he finds Cork too booring.
Anyway try to find something here:
http://www.in-madrid.com/default2.htm http://www.irlandaenred.com/content/tablon/8/profesores-de-idiomas To live here I would recommend you Villalba and Escorial areas because are beautyful, located by the mountains and there and there are frequent train services to Madrid city center.
Have a look here:
http://www.idealista.com/pagina/portada;jsessionid=660323176BCA3773C5FECA66F52F7D11.acaps3?opidiom=cidioma&localeRef=en
Good luck.