There are a lot of activities in Madrid that integrate learning and practicing English with leisure, sport, and cultural activities. Here are some ideas:

Sports in English
Bootcamp is a proven method to achieve instant results, gain endless health benefits and be the best you can be. In every session you will work your entire body with a combination of exercises designed solely to get rapid and long-lasting results. This sport is based on military training and consists of one hour of intense exercise: running, squats, boxing, strength training, et al without stopping. There are evening lessons with native English speaking teachers and foreign collegues in Retiro park.
http://www.bootcamp-espana.com

Cooking in English
MCH-Training offers cooking classes in English to give you the opportunity to learn new recipes, practice your English, and learn about the traditions of other countries. The lessons are completely in English and at the end of the course each student receives a notebook with the recipes and the vocabulary used. The lessons are in A Punto Centro Cultural del Gusto, in the center of Chueca.
http://mchtraining.com/idiomas-en-accion/cursos-de-cocina/
http://www.apuntolibreria.com/

Short appointments in English
Spanglish Exchange is a language exchange and cultural event founded in Buenos Aires, Argentina. It has successfully organized more than 800 affordable and fun events attracting both native Spanish and English speakers. In May 2011 Spanglish Exchange began holding events in Madrid. In each event there are 10 people (5 Spanish, 5 native English speaking) and 10 minutes to talk in each appointment, 5 minutes in each language. It’s 5 euros to participate and one free drink. But it’s not for flirting! 😉
https://www.spanglishexchange.com/

Playing in English
J&J Books and Coffee is a pub & bookshop located on 47th Spiritu Santo street and every Friday night at 11.00pm there is an open quiz English competition where about 70 people play to win and learn. The game takes place at the pub upstairs. On Wednesdays and Thursdays you can also practice your English with conversations. Downstairs there is a second-hand bookshop with more than 25,000 books in English that cost between one and four euros.
www.jandjbooksandcoffee.com

Night Meetings in English
There are a lot of pubs in Madrid that use nights to organize exchanges between natives and foreigners. For example, in Multilinkual Madrid Meetups, you can meet new people and practise languages with native speakers for free. There are Tuesday meetups at O’Neill’s pub (Principe 12), International Dinners for 15€ on Wednesdays , Thursday meetups at Beer Station (Cuesta de Santo Domingo 22) and Friday’s «Discounted Movie Nights in English,» with drinks at the 4D pub after every movie. At the meetings you’ll get to experience a lot of different languages and meet people of different nationalities. The meetups are especially recommended for expats and Erasmus students.
http://www.multilinkual.com/