Earlier quoted context omitted.
They most likely aren't ATA cables, as in, they aren't used to connect hard drives -- so it's not obvious that whatever purpose they serve could be served by a serial alternative. If you look at the photo of the back of the unit, you see a lot of very wide D-Sub sockets that these ribbon cables seem to connect to, so the unit is meant to connect to a bunch of other things. Actually, the need for these sockets seem to…
If you're designing your own boards with ribbon cables connecting them, I imagine that you could save a lot of money on parts by using 40-pin connectors with PATA cables--we're talking entire cents, for each of the 2 units. Also, I'm willing to bet a place like the BBC has boxes filled with spare PATA cables and 16MB SIMMs and 8 GB internal hard drives, and maybe even a room with a bunch of dusty 17" CRT monitors in…
Random BBC-related anecdote: the Cambridge University computer lab had, up to 1999, an info TV in the lobby driven by a 20 year old BBC micro in Teletext mode. This was apparently because it had an extremely powerful video output (more so than modern hardware) and the display was at the other end of 50m coaxial cable.