If I agree to an estate agent showing potential buyer/s my property but don't have a written legal agreement, do I need a HIP?

Yes. Provided the agent is marketing the property on your behalf, a HIP would be required and it would be the responsibility of the agent to ensure this.
Not having a HIP in place could lead to a £200 penalty for the estate agent marketing the property. This could lead to a banning order from the Office of Fair Trading if there were a number of such breaches.