That's the problem with back injuries - hard to prove whose fault it was sometimes.
Did it involve lifting/moving things? If it did then responsibility comes down to a couple of key questions:
1 Did your employer have a 'safe handling' procedure - including training in those procedures?
2 Did you follow those procedures? (this is where the reluctant witnesses come in!)
If the answers are both yes you do have a good case. If the answer to 1 is no and they haven't provided proper training where perhaps there should have been, then they've failed in their duty of care under the Health & Safety at Work Act. Looks like someone is just pussyfooting around, maybe the employer trying to bully you into dropping the case. You thought about taking them to an employment tribunal instead?
Last question - have you opened the darned letter yet?!
Best of luck whatever happens