A lot depends upon what you're asking and where you live. For instance, if you're inquiring as to whether you can actually draw blood from someone and then check his/her cholesterol in the state of California at your place of work, there are some restrictions against this being performed by unlicensed persons but you don't need to be a physician. This happens all the time at health fairs & exhibitions, etc (but apparently is not allowed in Nevada, I think).
On the other hand, if you're asking if your company can offer to pay for testing w/o going thru a physician, it turns out that yes, you can! There are plenty of private labs that don't go thru traditional insurance and just accept cash only. This allows you to maintain your privacy, say when checking for sexually transmitted diseases.
Of course, it also depends upon what your company wants to do with the information. I'm not sure that you're allowed to see the results from the company's perspective (protected health information, after all). Plus there might be some anti-discriminatory clauses against firing someone just b/c s/he has high cholesterol.
The caveat with all this is that you need to have someone interpret the results for you. That's where having a trained health care professional comes in handy. But realistically speaking, I know you could get good advice from a PA-C, FNP, and a nutritionist/registered dietician.
Ugh, I was afraid you were going to name someplace outside of the US. I'm not at all familiar w/medical legislation in the UK (or any country besides the US).
I do know that some companies make fingerstick devices whereby you can check someone's cholesterol (total, HDL, LDL & triglycerides) as well as glucose plus HgbA1c (running 3 month measure of sugar control) w/o physician's orders. These are the tests usually run during conferences here in the States with that type of equipment.
Occasionally, the vendors will actuallydraw blood, too, but this is always even more problematic since you need a licensed phlebotomist in addition to meeting all the stringent bio-hazard exposure/waste laws.
Wish I could tell you more about the UK. My best recommendation is to ask around your competition and see who's doing so and what parameters they had to meet in order to be allowed to do so.
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