Although there are two or three language schools in Leamington Spa, we would recommend Warwickshire College, which as well as providing many other courses, provides lessons for foreign students who want to learn English.
The college campus is close to to Leamington town centre and about 15 minutes drive by car from our house. Almost of our au-pairs have studied there and have been warmly welcomed into a friendly group of students and teachers. Afternoon excursions to local places of interest are a regular part of the timetable for a nominal fee and all day excursions to tourist attractions such as Oxford, London and Bath are arranged at weekends by the college for foreign students studying English. In the Summer the college offers an English language Summer programme- you can read about it here
The college is a good place to meet friends, particularly foreign students such as yourself as well as students from England studying at the college. Use of the college gym is available for all students for a small ‘pay per session’ fee. And there are many other student activities including discos, barbecues etc.