Can I countersign a passport application?
If you visit www.gov.uk - it provides a list of counter signatory advice for passport applications. Fellows of some institutions (now this one) may be Commissioners for Oaths, therefore they can countersign passport applications and sign passport photographs on that basis.
Furthermore, the guidance states that a counter signatory must work in (or be retired from) a recognised profession and be 'a person of good standing in the community'.
A list is provided of 'recognised professions', and these include being a member, associate or Fellow of a professional body. Members of most established institutes may satisfy that criteria, however you would be wise to check your status before acting as a counter signatory.
If you are in doubt, contact the passport office to discuss its requirements.