Slip and fall accident in a Restaurant, fractured wrist and forearm, can I claim compensation?

[Olivia]

Hi there, I've had an accident at work that wasn't my fault, I am employed at a the restaurant and I suffered a personal injury because of a hazard in the store that broke health and safety rules and protocol.

I slipped over and fell on a greasy food spillage on the floor that made the surface wet and slippery, falling over I landed on my arm heavy and heard a crack but didn't think it was broken at the time it was dangerous to work around and I get hurt as a result of an unsafe workspace.
After the incident it was recorded in the accident book by a manager, however I did not go and see a g.p or a&e right away, would I still have a claim? I never got around to it as I didn't think it needed medical attention and finished my shift.

It's still uncomfortable to bend wrist forward, I would say painful and when I went to see my doctor he told me I had a fractured wrist and forearm, its like a dull pain if that makes sense and It hasn't felt right for 4 weeks since the accident.
Can I sue Restaurant for my slip trip fall accident and the work related injury I suffered in their workplace?
And if so how much compensation could I claim of the company for my personal injury?

Helps appreciated

Thank you