The cheapest school I know in Madrid is called William's School on Calle San Andres (close to calle Manuela Malasaña which leads from Bilbao metro station). They charge 28 Euros a month for 3 - 4 hours a week (you can take more hours at a higher cost if you wish). It has basic facilities but does have native teachers in quite a few languages (English, Español, German, Chinese, Japanese, French).
One thing to be aware of is that wherever you enrol, there will be an extra 'matriculation' charge when first enrolling. THis is basically for admin costs etc. Also in the cheaper schools (and some of the more expensive schools)it is almost inevitable that you will have to buy your course book as well so budget for up to an extra 20 Euros.
If possible I would recommend you stay a month wherever you decide to learn the language. I realise it's hard to find the time sometimes, but it's worth it.
When you're out here you can practise your Spanish in one of the many language intercambios that take place. Madrid Cafe on a Wednesday night (after 9.30) is one - it has been mentioned in oter threads here. Molly Malones pub on Calle Manuale Malasaña is another (on Tuesday nights)
Enjoy!
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An English Bookseller in Madrid