I can find reference in the ANO to the register being maintained, but nothing related to the right making it available to any person to inspect. However the application form to register an aircraft states :
The UK register of Civil Aircraft is available to the public, including via the CAA website, and includes the names and addresses or registered owners of aircraft.
I don't know how this fits in with the Data Protection Act, but it does seem a little strange that the public can go online and get the address of the owner of an aircraft, when a similar tool does not exist for someone interested in knowing the owner of a car.
Agree with the above post though and think that the info should be available quickly and easily to those who need it such as ATSUs and airfield operators.