It seems this is a 'White Whale' for a few people and I know what looking for those is like (See signature >.>) so I did a little digging...
Angelina Jolie was indeed on this particular show, The Big Breakfast, an old breakfast show in the UK that went defunct in the early 2000's, but held a certain cult of fans as these things do, and has inspired some revivals in the last few years. However, Jolie was not on an episode on the date that original poster suggested... Instead she appeared a little earlier in the year on the 4th of July, 2001.
This interview was to promote the then new Tomb Raider film, and she was interviewed by Amanda Byram... and interestingly (and probably due to the shows quirky nature) this interview took place on a bed... which is probably going to get some of your minds racing.
However, there doesn't seem to be any footage of this episode online, although people definitely seem to have archived footage of this show and you can find the odd full episode here and there.
https://youtu.be /V3hcZ30tmbI
At 16:53 in this episode, you can see a VERY brief snippet of what appears to be the aforementioned Tomb Raider interview. That's the most I can offer you.
However, if anyone wants to keep investigating, and see if they can solve this mystery once and for all, there appear to be some guys on the internet who know this show well... I would maybe edge my bets on this guy
https://sites.google.com/site/bowlocksbigbreakfast/home who is a self-described superfan who even got to appear in the show in that capacity and keeps his fansite running and active to this day. He has Twitter, he has Facebook, (I have neither) and I imagine if anybody knew if this footage still existed and how it could be acquired it would be him...
Good luck, whale watchers! And maybe someday, someone will help me with mine...!
