I'm not a lawyer, so this is just my reading of the various documents of the SCC website.
The The application by Lord S's agent was in two parts:
1. to define his areas of land and the current rights of way across them, and
2. to apply to 'bring to an end any period of recreational use “as of right”, . . .' and also prevent such land being registered as a town or village green.
So the second part allows his representative to say "this is private land" (as it always was) but now he is ensuring that you cannot continue to use it for recreational use, just because you always have done.
However, this shouldn't have any effect on the current rights of way, such as Footpath Stafford 47, which is on the Definitive Map. You should still be OK to walk along the path as long as you keep to it, and don't let your dog wander off it.
I can't see any notice on the SCC website where the route of Stafford 47 has been diverted, and I've not gone into the SCC offices to check the Definitive Map, which is paper-only.
Perhaps a phone-call to the lady at SCC who put up the notices in December would clarify the situation?