Does a letting agent have to do an Exit Condition Report at the end of a lease?

It depends on your definition of a "letting agent" In the event the agent was only hired to lease the property and nothing more, than no the property owner should onduct this. If your question was managing agent, for example the agent whom the rent is paid to for the tenancy and ongoing then yes providing a bond was paid and an initial entry report (condition report) was conducted.