Why were you trying to work if you were signed off?
What sort of work do you do? If it is office-based, then it's probably feasible to work. If it's manual, then I can imagine you couldn't do the job properly.
I do not know if you can claim compensation, but an accident caused by a reported fault which wasn't fixed would imply yes, even if it was clearly marked.
I think it would weaken your case, or at least cloud the picture around how much of a problem it caused you, and thus how much they are liable for, that you chose to work, despite being signed off as not fit enough to work, but that is after the initial accident.
Did your employer know you were signed off? If they didn't know, I don't think you will have much of a case they can't be expected to make any adjustments until you're back to full health if they have no idea you should still be off work. If they did know, was there any discussion around whether you were capable of doing all required tasks, or whether you would need any support or adjustments while you continued healing? Were any adjustments agreed and implemented?
It sounds like they should have refused to let you return until your fit note expired, but it depends how much you told them.