It's in zone 2 on the tube map, I would still class it as central London, as opposed to greater London.
Maybe Martina who lives in London, or other londoners or british here can help us with this, but as far as I know, Central London is the zone where all the big monuments are, like the tower of London, London Bridge, The Monument etc etc. I think that district is called "City of London" or something like that, and often mentioned as Central London, as it is more or less the centre. The Studio is in Chiswick, in the west of London, quite far from the centre
It