Tracey . . .

If you were symptom free and the fall happened at work, then the w/c statutes in the UK might cover your injury/condition. However, if you did not file a claim for your injuries within the statute of limitations, that could make things more difficult, if not impossible.

If the stairs were in good repair, there would be no liability issues whether you were an employee there when you fell or not; but if the lights were out, the stairs broken, or some such thing, then you might have an issue to resolve with them.

If the fall did not happen at work, but your symptoms were aggravated by work, that is a tougher claim. Your work duties have to cause the condition in most jurisdictions, not just hurt while you are working, to be compensable. Excessive and repeated stretching and reaching can contribute to TOS.

It sounds like you had some tendonitis or carpal tunnel syndrome developing in your right arm/hand before your fall. Then you had a fall which may or may not have made this worse. However, unless you had already filed and established the right hand (thumb) symptoms as work related, they will now be seen as a pre-existing condition, even if they have continued to get worse. Most repetitive use injuries have a longer statute of limitations for filing, but you still have to establish a work injury in a timely manner to be compensated.

It sounds like you have left that employment based on what a therapist told you. Filing against a previous employer is even trickier, because now you likely have yet another employer who could be seen as responsible. The more time and activity that passes between a work event and the filing or assertion of a work-related claim, the tougher it is to prove.