Hello, I am a solicitor with over 15 years experience. I will try to help you with this.
Unless there is something in the employment contract with the person you suspect you can not require him to take a polygraph test. Polygraph evidence is not used in English courts, it being considered unreliable. I guess that because you want to use this test there is not much direct evidence of this person's guilt.
A final warning and then some vigilance of this person may be the best approach.
The money went from a safe in the security control room. Only security staff had access. Of a team of 12 people, only 6 had access to the safe on the given date. We do not wish to use the polygraph evidence in court, we just need to identify the culprit, so we can dismiss that person. The polygraph would be voluntary. Why would our HR not take the opportunity to identify the person. As for the other 5, whatever happened to innocent until proven guilty.
You can't force anyone to take a polygraph and the results would have no legal significance so if you sack someone on the basis of a polygraph test you will risk a claim in the tribunal. As for the last comment well yes I agree that would be v harsh, sacking a whole team because of the wrong doing of one person.
All 6 have volunteered to take the polygraph, but obviously one person is bluffing, thinking we won't do it. If the employer dismissed all 6 security officers, would there then be a case for unfair dismissal.
You are moving into a different area now. There might be a risk. But remember polygraph tests are not considered reliable evidence. Sack someone for failing the test or refusing to take such a test and you will very likely have a claim.