There are a lot of places you can learn BSL. To locate a course you can contact your local deaf club (google the name of a major town near you and deaf club), look at the adult education prospectus or look on Signature's website for a list of all all accredited training providers.
What can you expect when learning BSL?
Well, typically, you will start by doing a level 1 course and you will learn the basics - fingerspelling, places, things in the house, work vocabulary, colours, weather, holidays, animals, and basic grammar. You may be taught by a Deaf BSL user or by a hearing person with a good knowledge of BSL. In the classes you can expect to go over new vocabulary each week, produce stories, and chat with others in your class. All this should be done in BSL with your voice turned off.
You may then do a bridging course, which will improve your skills to nearer that of a level 2 class. After that you can take the level 2 qualification, this will build upon your vocabulary learnt in previous courses, expand your knowledge and ability to use BSL grammar, try to move you away from using Sign Supported English (BSL signs produced in English word order), improve your receptive skills and increase your confidence. It now becomes more important to turn your voice off and to use BSL in each class. Once you have your level 2 you will be able to hold a conversation with a BSL user.
Once you have achieved your level 2, you need to use your BSL regularly and try to mix with Deaf people in order to improve your productive and receptive skills. The next stage is a level 3, and typically you will have spent at least one year if not two practicing your skills and using them regularly. There is a huge jump between the level 2 and level 3 and to help you improve your knowledge you may want to consider doing a pre level 3 course. This is where I am at now, and I can honestly say that the pre level 3 course I took was invaluable and worth every penny I spent. Without being in a formal classroom situation you won't realise what bad habits you have picked up and what it is that you don't know.
After you have achieved your level 3, you will definitely have a good handle on the language and be able to explain and communicate complex ideas in BSL, not SSE. Next up is the level 6 which will take you to interpreter standard.
When you are learning it is important to practice outside the classroom as much as you can. You can do this with friends on your course, or go to coffee mornings or other practice sessions at your local deaf club. You may want to go to interpreted theatre performances to improve your receptive skills, or you can watch the BSL interpreted news on BBC news 24 at 8.30 am and 1pm (I think). See Hear is a good programme about the Deaf Community that is viewable both on BBC 2 and the i-player, if like me you don't watch TV. Like any other language, it is important to learn about the culture of the people who use BSL as it will help you to understand ideas and structure within the language.