I am after my fellow professionals opinion on the following:

We are an independant consultancy, one of our clients wishes us to carry out site audits on their behalf. Our client is a contracting company that works on the site of principal contractors. Under normal circumstances when we visit a site on behalf of our client we will liaise with the principal contractor when we arrive and explain to them the reason for our presence on site, as part of the site audit we will ocasionally ask for a plant operator, eg excavator driver or person on MEWP if they have their card (CSCS NPORS )with them and we will just check to see if they are OK to operate the equipment they are using and to establish if the card is still in valid date. Also as part of our audit we will check things such as the CPP is being kept up to date, the F10 is still in date, sub contractors risk assessments and training records have been obtained and kept on file ect. I have done around 15 of these for this particular client (plus many others for other clients using the same format) and have never had an issue until recently. One major contracting companys Health and Safety manager took exception to me asking to see the operators competence card and some of the documentation of theirs. The question is:

Am I in my right to ensure that from our point of view ( on behalf of our client ) any person operating plant and machinery in an area where our employees may be affected is competent to do so ?

And am I right to ask to see certain documentation, again to determine that the PC is adhering to their legal obligations and not putting our clients employees at risk.

I'm unsure from you're post whether or not the operative you asked for proof of competency from actually worked for the company you were undertaking the audit for?.
If the answer is yes, then most certainly, its within you're brief to ask for sight of his certification, whether directly or through the operatives supervisor.
If the answer is no, and he works for someone else, i would make the request via the principle contractor.
You have no authority to undertake a competency check for anyone other than you're own client, other subcontractors and their employee's can get quite shirty when approached for this kind of information, and whilst i understand you're requirement, the request should be dealt with differently.