I don't have Sky but I've just been looking through the Sky TV website and I can't see anything like "The satellite dish remains the property of BSkyB plc . . ." in their terms and conditions. As far as I can see, the dish is yours and, therefore, expecting Sky to remove it is a bit like expecting the BBC to come and remove an unwanted aerial for terrestrial TV.
I don't think that anyone needs to remove the dish. It can just stay there, unused. The only exceptions are as follows:
A. If your old house was rented and your landlord only permitted you to install the dish on the understanding that you'd remove it when you left, then it's up to you to remove it (either yourself or by employing someone to do it for you).
B. If you've sold your house to the new occupier, and the sale agreement which you signed stated that the dish would be removed, then, once again, it's up to you to find a way to get it taken down.
If you haven't entered into any agreement, either with a former landlord or with the new occupier, then the dish can stay where it is. If either the landlord or the occupier, as appropriate, doesn't like it being there, it will be up to them to remove it.
Chris
PS: Even if the dish is actually the property of SKy, there's unlikely to be any responsibility upon them to remove it. They mave have provided a free, or discounted service, to put it up but this doesn't oblige them to take it down.