Hi Lisa,
As a HIP provider myself I can tell you that HIPs for leasehold properties do cost more to compile so the agent may well be telling the truth in that regard. The agent should know this too but many do are as yet unfamiliar with leasehold properties since most leaseholds are currently exempt from HIPs (one and two bedroomed properties).
Having said that the price they have quoted even for leasehold seems overinflated. You could certainly save money
As Conmankiller quite rightly says: the thing about HIPs is that generally speaking if you order and pay for it yourself then you own it so you can take it to any agent you like so its 100% portable between agents if you become unhappy with them. Since you've signed a contract with the agent, your contract will tell you if you can pay for your (updated with leasehold documents) HIP and take it to another agent.
You can indeed commission your HIP from a Solicitor or alternatively find a dedicated HIP provider.
Hope you find your way out of this tangle. Regards,
Chris.
Happy to help.