Some of the information is harder to come by because none of the studios at NBH (with the exception of Studio V) can be hired out by external client, whereas the main block studios at TVC were commercially available, hence why there were floor plans, tech specs, drawings and decent images. I’ll have a look at the Wikipedia page and see if there’s anything majorly wrong that I can explain.
EDIT actually it looks relatively up to date to me.
Please feel free to ask any questions or clarify anything.
Studio V isn't marketed in the way BBC Studioworks or BBC Resources studios were either, and hasn't ever, to my knowledge, been hired by an external client (though I may be wrong) other than RTÉ, and that was a slightly special case due to the close links between the BBC and RTÉ and the BBC International Unit.
It's a grey area - but Studio V is effectively fully funded by BBC Studios for The One Show (and also used for other BBC Studios shows like Sunday Morning Live, Front Row Late, Rip Off Britain Live, Healthcheck UK Live etc.). The studio is technically owned by BBC Content, and managed by BBC D+E, but the day-to-day management of the space is mainly handled by BBC Studios and D+E.
The only independent production, I think, to use it has been the now-defunct 'This Week', made by Juniper, which itself was a special case as they usually used the BBC Millbank studios (and I believe the BBC resources were, unusually, included as part of their commission). In that situation the change of studio was handled internally within the BBC - and Juniper didn't really get involved AFAIK.