Yes, but X Factor don't use the space half as well as BGT. Got Talent looks like it's filmed in a studio twice the size of X Factor, and then they make it even bigger with More Talent upstairs.
It all just feels a lot less cramped than X Factor. Maybe the lighting plays a part too?
But it looks more spacious for a reason. BGT needs a larger performance area for all the dancers, acrobats, magicains and group acts, whereas TXF only needs a smaller stage as most of the time it's just one singer (who remember is always there last chance at making it....) standing there, singing.
Studio 1 at LWT would be no where big enough (they would have to remove the lower tier of seating to get the stage and camera run in - and the raised judges table. Studio 1 at
TVC may just be big enough, if the stage ran length ways (so the dock doors were to the left of the set).
The only other option left is the sound stages at Pinewood or Shepperton. At Pinewood, TV1 and TV2 are mid sized studios, although the makers of Beat The Star seem to have found a chucky studio to make series 2 in (can TV1 and TV2 be joined together like Fountains studios can?) .
That leaves Shepperton. Only problem there is there are no tech facilities on site (in terms of kit and control galleries) so everything would have to be done via an OB truck parked out the back - leading to more expence.