Hi, The BBC does have this in it's archives.
I recently found out that contributors for programmes can apply for and purchase DVDs of shows they contributed too. As I was one of the kids who wrote in asking a question of Mark I was able to buy a DVD of the show for £108... it is worth every penny!
The show was recorded and aired on the 20th of May 1980 "Empire" Day and Mark talks about "Revenge of the Jedi."
I remember watching Blue Peter and have no recollection of Revenge of the Jedi being mentioned. Also, if I remember correctly, Ask Aspel was shown first. But it was 34 years ago....
Unfortunately, I am not allowed to copy, share or even lend it out!