It would be necessary to demonstrate that the people undertaking the inspection have sufficient knowledge to undertake the work. There is a Ministry of Justice publication entitled "Managing the Safety of Burial Ground Memorials - Practical advice for dealing with unstable memorials" which provides useful guidance, including the following:-
"Visual and hand checks can be carried out by a person with a working knowledge of memorials and their defects, and/or good knowledge of the memorials in any burial ground, but those inspecting memorials need to be mindful of, and consider, the risks to their own health and safety. Hand testing is appropriate for many memorials, such as the modern, lawn type, as well as smaller stepped designs or tiered crosses. Much larger, heavier memorials, such as older columns or obelisk types, may require an assessment by a specialist engineer or competent memorial mason."
The guidance states that:-
"The hand check can be carried out by standing to one side of the memorial and applying a firm but steady pressure in different directions to determine to what degree if any the headstone is loose. If some instability is detected following the hand test, a judgment must be made as to whether this movement is limited, or whether there is sufficient movement for the memorial to present a high risk to people’s health and safety."
That judgment would need to be sufficiently robust to stand up to examination in a court of law. Personally, I'd steer well clear and leave it to the experts.