Are there any University rules covering consulting to a spin-out?

Yes. The University’s consultancy policy and procedures formally states:

“Staff who are founders or directors of spin-outs are required to use Oxford University Innovation’s Consulting Services for managing consultancies to their spin-outs in the first year following formation of the spin-out. After that 12 month period, staff may choose to continue to consult through us or to consult privately/independently.”