There are 614,000 teachers in the UK. The BBC employs just 21,000 and last time I checked the head of teaching didn't have 800+ images on kiddy porn on their computer and none of them did the numbers of Jimmy Saville.
It's almost good that you brought up Jimmy Saville, pretty much the only investigation into him at the time of the offences in the 70's was attempted by and you'll never guess, the BBC. The problem was the person that raised it couldn't name the alleged victim or give any details sufficient for the BBC to proceed with any more (IIRC the person that raised it wasn't even a first party witness).
Meanwhile for decades afterwards he was actively abusing people in hospitals where it was hushed it up despite nursing staff warning each other, and the police received multiple allegations that they didn't bother to follow up on other than to tell the victims to stop making stuff up.
It is worth looking at the statistics for teachers and school staff who have been found to have committed offences BEFORE enhanced checks were done on anyone who worked at a school, even just contractors who would be working on the school grounds, and consider that the BBC does not in fact have to have it's staff vetted (although IIRC they do for staff who will be working around kids). IIRC the BBC also mandated chaperones for known under 18's years before there was a legal requirement.
Guess what, the stats for abuse offences before enhanced vetting are not great for education, especially anything from before the 80's, and there are still routinely cases of school staff being struck off, banned from working around children, and convicted because of things like having sex with their pupils, but unless it's something really horrific it tends to get a brief mention in the middle of the papers, or on the local section of the news.
I remember a couple of decades ago a senior doctor at my local hospital, who specialised in paediatrics was found to have been keeping indecent images of children in a locked file cabinet*, IIRC I don't think it even made the nation papers, my parents only found out because it was in the local paper at the time and they recognised the name.
I've been reading a lot of various news websites, especially in the "local" sections and every few weeks there is another story about a teacher being struck off for inappropriate behaviour, or a medical professional, or a police officer (all three groups have far better vetting that is legally required than the BBC ever has), literally every week there is a story, but guess what, they're on the "local" news section because the people involved are not well known names so despite their offences often being as bad or worse their names aren't over every paper and on every news channel.
So yes, once again I'll point out you hear much more about one BBC related case than you would any 10 other cases of a similar level simply because if it's someone that works at the BBC, let alone a "face" or "voice" it makes a nice story that will get clicks to websites (or back in the day, sell copies of the Sun/Express/Mirror where they'll do a count down to a celeb "being legal" under a story complaining about how TV/music/film is sexualising children).
*IIRC the story goes that he was on holiday there was a need to move the cabinet due to a leak or something (I can't remember if it was a leak or they'd got new filing cabinets/moving them), so his secretary had to empty it and found the folder with the pictures behind one of the drawers.
