TIL one of the oldest TV shows was simply called "Sea Stories" on the BBC, featuring Royal Navy Commander A.B. Campbell describing the personalities and places he had seen. No known footage exists.
It's frustrating the image for that article is of the 4th Doctor, given the BBC had stopped erasing tapes by the era of the 3rd Doctor. There are no missing 4th Doctor episodes.
taping at a corporate level didn’t exist until 20 years after the OP’s show aired – and another 20 years until consumer taping entered the picture
even then, BBC had no compunction about continuing to erase stuff – only relatively recently, they’ve started to realize just how bad a decision that was and have been begging for copies from people who taped shows to VHS – which itself hasn’t gone over too well because BBC also has a reputation of prosecuting home tapers, so without a promise of amnesty, no one’s coming forward …
Given that reel to reel tape recording of television didn’t begin until the 1950s I’m going to say they didn’t. The only way they recorded back then was pointing a film camera at the TV, but this couldn’t really be used for rebroadcast, so I’m guessing a lot of these early TV broadcasts weren’t recorded.
Early days of television was the wild west. They didn't know what to do so they basically took stage and radio concepts and adapted them to TV. That's why so much early TV was vaudeville-esque variety shows.
But they didn't even have a means to record if they wanted to. Everything was live. Not even a delay.
There was a podcast episode about this recently, and Howdy Doody...I think it was 99PI.
It’s basically like Anime, the tv shows do exist but no records were saved. You could try to find any source of advertising or something that connected with the tv show.