"You can't book an initial appointment by phoning..."
About: Moorfields Eye Hospital (City Road) Moorfields Eye Hospital (City Road) London EC1V 2PD
I just tried to book on the phone as they operate a 'telephone booking service', you have to actually fax in a letter from your doctor, this is not clear until you call in.
Fax number is 0207 566 2351
Please note I haven't visited yet, this is advice on appojntments that I'm making available online as the booking process is not obvious.