Scheduled monuments belong to the landowner but they are legally protected so no-one, including the owner, can damage them.
70% of land is also now subject to DEFRA Stewardship schemes whereby the landowner gets paid loads of money to ensure natural and archaeological assets are protected and loses the payments if he doesn't. If you climb on top of standing stones on land that's subject to such a scheme the farmer may not be prepared to listen to the "research" excuse. On the other hand, if you do it right and ask him and Defra in advance they'll probably agree. Simple really.
As for getting a full consensus on a Code, that's going to be impossible, as this thread shows. On the other hand, I bet 99.99% of people would say climbing the Devil's Den is a no-no so a pretty serviceable and well supported code IS perfectly possible. Indeed, one of the suggested clauses covers DD quite well - Act with respect towards the feelings and enjoyment of other visitors.
Codes are fine if you can uphold the objectives but other than the flagship sites who is going to overseee the forgotten and remote ones? Yobs and louts won't give a toss and you take your life in your hands addressing some of them when surrounded by their often tanked-up mates. It would only carry the weight of a Code of Conduct such as 'No spitting on this bus' in effect as you'll never stop anyone from doing it unless the penalties are so severe that it frightens the life out of them...and that won't happen will it!! As my old dad you to say God bless him...'Bring back the birch'!