Maxwell Knight (1900-1968) worked for MI5 from 1931 until after World
War 2 when he started a second career as a radio and TV broadcaster.

He was an amateur naturalist and wrote several books. 

It has been reported that he appeared on the TV programme 'Animal,
Vegetable & Mineral' and, on radio, as 'Uncle Max' in 'Childrens' Hour', among
others.

Can anyone tell me specifically WHICH TV and radio programmes he
appeared on and when?

I think the radio program he broadcast on was the BBCīs “animal
vegetable OR mineral” ie. not “animal vegetable AND mineral”

Yes ... It probably was the BBC TV programme 'Animal, Vegetable or
Mineral' but when?

Are you sure about Uncle Max on Children's Hour?  The only references
I have found are to Uncle Mac, Derek McCulloch, eg
http://www.sterlingtimes.org/children12.htm

Actually “animal vegetable or mineral” was both a radio program and a
TV program, although the radio program was a comedy type show so I
think that puts it out of consideration.
I researched your question for quite sometime but couldnīt find any
firm evidence in terms of names or dates.  All I can say is that
“animal vegetable or mineral” started in about 1952
http://www.upenn.edu/museum/Games/whatintheworld.html
Have you tried an enquiry at the BBC ?

I have found this site to be quite useful too
http://intellit.muskingum.edu/intellsite/maintoc.html the alphabetical
listing is very useful too
http://intellit.muskingum.edu/intellsite/alpha_folder/alphatoc.html

I have already e-mailed the website author asking him to correct his
Union Flag in the United Kingdom section and to correct his entry
regarding the SBS, and have received a reply saying that he was going
to make the changes at the next update.  I found the website owner to
be very friendly and itīs possible he would be willing to help in your
research by e-mail (although I havenīt mentioned this too him)

Good luck in your ‘mole’ hunting

THX1138