Do logged hours with a Sport Pilot instructor count towards a private pilot certificate? I've my Sport Pilot licence and I've got logged hours with a sport pilot instructor that isn't a private pilot instructor.

Can I use my logged instruction hours in order to upgrade to private pilot?
No.  Sport pilot instructors are not authorized instructors with respect to private pilot certification.

See 61.109(a).

The FAA has issued a legal interpretation on the matter.  See the Kern Ink interpretation