Why not look into local providers of BSL classes and ask their advice about learning and beyond?
I did part of a BSL course when I was at uni although couldn't finish it due to my degree commitments. I found it a huge help (as with any language) in communicating with deaf people and using sign language on a more day to day basis, it makes a massive difference. I used to do quite a bit of voluntary work generally so it came in very useful at times.
I picked up a lot just by doing some volunteering at a local deaf club and a lovely gentleman who lived locally where I studied who would often come in to where I worked locally, cafes etc... and chat (sign) away - it was great as some of the other staff would then pick things up and be able to communicate with him better.
I also did some residential volunteering with Winged Fellowship (now Vitalise) and helped one lady in particular who is deaf and blind. Obviously it is different signing (mostly on hand) but doing it on a day to day basis meant I got very quick, would even translate phonecalls for her etc...
Student tutoring could also be a possible - I assisted a blind student in mainstream schooling for a while on a voluntary basis as well as helping in the special needs unit with reading etc... in lunchbreaks. There may be an opportunity to help with a deaf student (maybe even in FE or at uni, taking notes and general support and assistance). This kind of work could also give a useful insight and skills for a teaching career.
Remember many deaf people are expert lip readers so you can communicate as you learn pretty well so, as long as you have the right attitude towards it, don't be put off until you feel you can sign to a certain level.
So look into local deaf clubs you could volunteer at and maybe organisations which run holidays for the deaf you could help at etc... It could make a big difference to how you progress.
I was part of a volunteering group who had all kinds of opportunities so maybe if you have a local one, they could help and maybe find opportunties for you.