Arguably the pre-eminent quiz show in the UK (in terms of longevity, having famous people on, and being on TV). I thought it would be good to type the presenters and many of the most frequent guests as a mass-exercise and due to the possibility of typing the various interactions.

Socionics.com has the following typings for the three longest-associated people:
Angus Deayton: IEE
Ian Hislop: SLI
Paul Merton: LSE

I think the Hislop typing is correct, the Merton one may well be correct but he'd be an interesting person to discuss, and the Deayton one...don't really know but it doesn't seem problematic.

Guest by most appearances (I will perhaps try to endeavour to type those I haven't in the future):

24 appearances:
Alexander Armstrong: maybe LIE

16 appearances:
Ross Noble: no definitive opinion. Probably uses / appreciates

14 appearances:
Jo Brand: I think ESE, SLE may be possible
Andy Hamilton: SLE

13 appearances
Marcus Brigstocke: LIE
Kirsty Young: no definitive opinion

12 appearances:
Jeremy Clarkson: SLE
Martin Clunes: no definitive opinion
Jack Dee: I previously thought LII for ages, maybe Delta ST is more appropriate
I was thinking for some reason that he reminded me of Martin Freeman in terms of dress and demeanour.
Ken Livingstone: typed as IEI by @Expat - could work

11 appearances:
Reginald D. Hunter: no definitive opinion

10 appearances:
Clive Anderson: : no definitive opinion
David Mitchell: ILI
Frank Skinner: maybe ILE

9 appearances
Danny Baker: some type?
Germaine Greer: no definitive opinion
Charles Kennedy MP: ESI ( I can't remember if I came up with this typing or Expat did)
Will Self: an incredibly morose individual that I'd like to know the type of
Mark Steel: I thought IEI before but I'm not really so convinced. Utterly fascinated by him...
Janet Street-Porter: no definitive opinion

8 appearances
Victoria Coren Mitchell: only a vague impression, so: no definitive opinion

7 appearances
Bill Bailey: no definitive opinion
Gyles Brandreth: no definitive opinion. probably few or no non-UK people will know who he is which is shame but he's an individual I'd really like to know the type of.
Dr Phil Hammond: feels like he is probably a ExTx type
Julia Hartley-Brewer: no definitive opinion ( I barely know who she is)
Boris Johnson: ILE
Miles Jupp: only a vague impression

(more to follow)