susan hudson: The TV Licence permits one to view broadcast programmes and gives no warranties as to availability of signals and no assistance to receive any available signals.
The Public Service Broadcasters, which includes the BBC to which the Licence Fee goes, must ensure that most of the population can receive its services via a terrestrialaerial. There are always spots where reception isn't possible, either because the terrain precludes it or because of another obstruction such as trees.
In your case you are most unfortunate if you cannot receive any digital terrestrial (Freeview) signals particularly if you could pick up the former analogue. Was the analogue poor? I imagine that it might have been affected as the wind blew the trees and probably worse in summer when leaves were on the trees.
There are two main satellite platforms: Sky with its subscription service (although it does offer its own "Freesat from Sky" service) and Freesat. Freesat (not to be confused with "Freesat from Sky") is the satellite equivalent of Freeview - there are some channel differences.
You say you had Sky round to look at putting up a dish. I'm not familiar with Sky but I wonder whether engineers have limits as to what they will do. For example, if in your case it is possible to receive a satellite signal but the dish would need to be mounted on a very long pole above the roof line, would a Sky engineer go to this length? If the answer is "no" then you need an independent rigger who can fit the dish high up.
However, if you've already had a rigger to look at installing a terrestrial aerial and he's said it's not possible, I imagine that he may have also pondered the possibility of satellite reception and come to the same conclusion.
As I understand planning law, it not legal to mount a dish so that it is above the line of the highest point of your roof, excluding chimneys. If the roof is a typical ridged design with a row of tiles along the top, the dish may not be above that. So it should not be mounted above that on a long pole that would sway in the wind and give variable reception.
Best to ask you local Council Planning Department for advice on mounting dishes in your location.