I don't think so.
I emailed IPS a while back about acceptable people...the following snippet may be relevant from what they posted me
If a professional person has not retired and no longer works in the field their qualifications relate to they cannot sign. The exceptions to this are members of professional bodies e.g. Chartered Accountants, Chartered Surveys, Solicitors, Barristers etc. They can countersign and state that they are retired or non-practicing and then give the name of the professional body to which they belong.
I think the essential criteria in general is that counter-signer belongs to a professional body (thats why teachers, doctors etc can sign).
Holding a BSc(hons) is not membership to a professional body. I don't think you can counter-sign the application.