Regardless of the cause of the accident your employer has not handled this correctly. There should be clear guidelines for investigating/ recording accidents at work, and a risk assessment for you working at home, this accident should have been reported to RIDDOR as well. Does your employer have anyone that deals with health and safety within HR or facilities?
You can not lose your job for making a claim (over 1 year), many people do, win and continue working for that employer with no problems at all.
What did the cause fall anyway?