'tis the season to be bored (fa-la-la), so I relish the opportunity for a little bit of legal sleuthing.
I've had a reply from my friend (hello Martyn, if you're reading this), with a wealth of general information and useful pointers.
Criminal liability first.
Desecration. There is no specific offence of "desecration" in English law. There is a relatively minor offence of removing a body from a grave without lawful authority (Burials Act 1825 S.57), but this carries only a fine of up to £200. Significantly more serious is the act of removing a body from consecrated ground (ie digging one up and taking it out of the cemetery or graveyard, rather than just moving it to somewhere else), which is an indictable offence (R.v Lynn, 1788). Nothing about damaging a headstone though, unfortunately.
Criminal damage. This would be an intellectually challenging avenue to pursue, but of little practical purpose. It would be necessary to prove beyond reasonable doubt that a particular limited company, or a particular person caused the damage intentionally. A lot of effort, for little practical benefit.
Damaging a Scheduled Monument. This one could be interesting. Is this cemetery designated as such within the provisions of the Ancient Monuments and Archaeological Areas Act 1979? It may well have been. However, there are also some statutory defences to an allegation of an offence under this Act. It would first be necesssary to identify that the cemetery is covered by the Act, before undertaking further research.
Now on to civil liability.
The general proposition is that a civil action can only be brought by the person who has been wronged. Who has been wronged in this case? The person (or legal entity) who is the legal owner of the headstone. That's not as simple to identify as it sounds.
Given the age of this cemetery (it certainly predates the Cemeteries Act 1933). Is it on land owned by the Church of England? If not, it would almost certainly have been established by its own Act of Parliament. In either case, the relevant instantiating legislation will contain provisions relating to the ownership of burial plots and grave ornaments in the cemetery. There are many scenarios. The plot could have been purchased outright in perpetuity. It could have been purchased for a term of years, after which the plot and all ornaments become the property of the owners of the cemetery itself. It could have been subdivided, with sections being sold or leased to other organisations within the geographical area (this is a distinct possibility, given the military connections). It could have remained in the ownership of the cemetery authority, with a license to bury and a right of perpetual access. Only one thing is certain: it will be owned by someone. Thanks largely to the Normans, every square inch of land and every atom of every good or chattel is owned by somebody. You just need to find out who. In extremis, it would be the Crown.
Having established who actually owns the headstone, we must consider whether permission (express or implied) has been given, and whether that permission covers the damage that has been done. In some ways it is analogous to trees hanging over a boundary fence: you have the right to cut back the trees to the exact boundary line, but the branches must be given to the owner - they are not yours. The same applies with the headstone.
Assuming permission was given, to what extent? Was it permission to move any obstacle in the way of the fence? To smash any gravestones they disapproved of? This is a question of what is reasonable in the circumstances. Given the equipment that the fence-erectors would have had on site, I think it would have been far more reasonable for them to have lifted the gravestone (or cut it off at ground level) and laid it flat. Or possibly to have set it upright again. But I'm not deciding this case, and my opinions are not worth the paper they aren't written on.
All in all, a very interesting situation. If you want to pursue it further you will have to do a few things: ascertain whether the cemetery is scheduled, and identify its establishing legislation (either ecclesiastical, if CofE property, or by Act of Parliament). Your best option is to identify the owners of the cemetery (I think that the owner of a cemetery is required by law to have contact details clearly visible on or near each main entrance), and then make sure that they are aware of what has been done.
Sorry for the long post, but I think that the circumstances justify it. Now I'm going to have a cup of tea.