I cannot see why the BFR, which is formal content of 1 hours flight + 1 hour ground school, should not be acceptable......
From JAR-FCL 1.005
(2) Whenever licences, ratings, authorisations, approvals or certificates are mentioned in JAR–FCL, these are meant to be licences, ratings, authorisations, approvals or certificates issued in accordance with JAR–FCL. In all other cases these documents are specified as e.g. ICAO or national licences.
Therefore a flight with an Instructor means a JAA Qualified Instructor. If your BFR instructor was so qualified it can count for both.