Please could you list any places where I could find work experience in Leeds/Bradford etc. Any bank, law firm etc.
They're not likely to take you on (banks/law firms) because they're professional jobs where they don't have the time to look after a work experience placement. A very small, local law firm might let you on but im pretty sure no bank will.
Ok, any other places?
I managed to get work experience in York, in a very local law firm. They only have branches in Pickering, Stamford Bridge and York. Your best bet is to email/phone the local places and specify that you are willing to just fetch coffee if that is all you're allowed to do. Another reason law firms might not take you on is confidentiality problems. If you let them know you take client confidentiality seriously and you're willing to sign something saying you won't go and blab your mouth to the first person you see, it's more likely somewhere will let you get some work experience.
Also, the place I'm hopefully going to (got an interview with the partner), didn't advertise work experience placements nor do they usually take people on. So you literally just need to find the emails/phone numbers of local law firms (there will be some) and speak to a lot. I emailed 6 firms before one even considered me. And at the one firm I am able to go to, I emailed 6 different people over two of the branches.
You just have to keep trying.