Depends on the broadcaster. Sky uplink their own services, and those of others from at least one location (which they inherited, or the use of, as part of the BSB merger I think - though I may be wrong)
Yes they have their uplinks there at Chilworth in Hampshire, the teleport the IBA built for BSB, although much expanded. They also playout some of their channels from there and it was home of Sky Box Office
The other IBA site down that way at Crawley Court is one of Arqiva's major teleports. Presumably there's some uplinks from there some third party downlinks too, I know of one broadcaster that rents some dishes and remote controls them from their studios in London
The BBC uplink their own services, mainly, though they may also use third party uplinks for some services.
Yes, it uplinks its domestic services but not international ones presumably because that needs uplink sites around the world, it can't all be done from the UK