Ok further to my question on your post. The reason is, I asked the same question for the specific scenario you gave awhile ago.
If you have access to the members area the link is
http://forum.iosh.co.uk/posts/m771822-Electrical-equipment-contractors
I hope this helps. I also had a lot of help and discussion with Paul, who by now I owe several pints (in fact probably enough to make him fall over).
With regard to the general concept of how to determine competence, that is even more tricky as noted above by everyone. To an extent it goes down to gut feel, yes ok if there is some sort of trade association etc then that may help, but you will still get good and bad. The other problem it is unlikely that the H&S bod will be the one picking the contractor or placing the contract. Those that do will have other selection criteria (£).
So, who ultimately decides if they are competent, I would say the judge in court when they decide they were not competent? Which is also of no help. The only way you can satisfy yourself, is by giving new contractors a less critical job and see how they get on. But of course, you are brining them in as an expert and so you will not necessarily know the in and outs of electrical installation, but you can judge the general way they seem to be working. If you have been using someone for a few years and the machines get fix and work, they appear to you to be working in a safe manner, then record your evaluation. I will not stop them doing something stupid in future, but there is a limit of what you can do (and ask others to do) when selecting.
Some are easy, like gas work, building air con, operating a Chery picker etc, others may have more than one possible qualification to go with experience, in fact the more experience probably the older the qualification will be (ie not the latest), certainly electrical work fall into this type. Then there will be other almost unique odd ball things and that will be down to your best view and gut feel.
I think asking for references is old hat now, same as job references. Lots of companies don’t want to put anything one way or another down in writing in case of some sort of comeback IMHO only.
So, like lots of things work related, you know when you have got it right as nobody is giving you a b@11@cking for it being wrong.
Now try and write that in your ISO procedure :0)
Chris