I know major airports like Heathrow are officially safeguarded ,which presumably means obstructors can be prosecuted ( although I've never heard of it happening
The Safeguarding process is there to prevent new buildings being put up that penetrate various obstacle surfaces. Up to the mid 90s the Local Planning Authority would refer applications that would penetrate such surfaces to the CAA but this was then devolved down to the individual airports. All the airports could do (and the CAA before them) is object to the LPA. If the LPA decided to permit the development and thus adversely affecting the airport then they would then have to ask the Minister to call in the application for consideration. Never happened in my experience (I was responsible for Safeguarding at Luton for a number of years).
What the Safeguarding process didn't pick up on was the cranes needed to build the new building and in my experience crane companies would often supply the biggest soddin' crane they had on their books. There isn't a law to prevent someone putting a crane up even right on the final approach. There is a British Standard that says crane operators should consult with an airport opertaor if they wanted to raise a crane within a certain distance of an airport (4nm I think) above the surrounding trees and buildings. Most didn't in my exprience. All you could do, as SRG told me, is to threaten them with Article 73 (Endangerment) and being criminal law ask a policeman to intervene. I tried the threatening but not the policeman.
Same would apply to airfields and strips not safeguarded and unlicensed. You could say 'If you put that obstacle there you are contravening Article 73 and I will inform the police'. Not too sure what the police would do however! Obviously to mitigate the 'danger' you can opt not to operate and my fall back was to suggest we would sue for compensation of £10,000 an hour (a figure I plucked out of the air at one meeting with a local company who had put a crane up with no consultation). It worked.