In the U.K. the Health and Safety Executive collects workplace accidents and fatalities data. They publish aggregated summaries but not the raw data.
How and to whom do I request the raw data?
Probably the easiest way is to make a freedom of information request via WhatDoTheyKnow.com.
You will have to be very careful, however, to phrase your request in such a way that they cannot reject your request on the basis that the data might allow you to identify a living individual. You can avoid this problem by making sure your request is tightly focused on the data you want for your project.
For example, if you want to look at whether rates of accidents vary across days of the week in different industries, you should request only those fields that you need for each incident (e.g. the industry and the date of the accident), while not requesting the location of the accident (since you might be able to combine that with the date to identify a person). More detail about how to make a good FOI request is available.
One benefit of using WhatDoTheyKnow over making an FOI request by email is that other people will be able to see (and use) any data you get. If you're not comfortable with that (e.g. because you're a journalist and you want a scoop) then you may prefer to make the request by email.