I drive an old manual Toyota Tazz (2002 model). It came back from it's last service months ago with a "spring-like" / squeaky noise every time I turned my steering wheel. I queried this with the service garage but was told it was nothing. The other day, in damp weather, I was driving fairly slowly but when I applied brakes my wheels locked and the car skid, so I took it in to a drive-in brake centre, thinking my brake pads needed replacing. I was told that my brake pads were in good condition but that the parking brake cable was about to go. By the time I had driven around the corner to the repair garage it had snapped. Now that it has been repaired, the squeaky / spring-like noise when I turn my steering wheel has disappeared and the car seems to have a much better grip of the road. Does this make sense? Would a worn brake cable have affected these things? I would really appreciate some insight as I haven't been able to get a clear answer from anyone I have asked. Thanks.
A worn parking brake cable wouldn't account for the squeaking noise in your steering. It also wouldn't cause your brakes to lock, or effect your grip. It's possible that your parking brake wasn't releasing, which you may have been noticeable with the handling but not the other things you describe.
Fixing the parking brake cable could very likely resolve the braking/handling issues you were having because it involved disassembling the rear brakes and hubs to get at the cable connections for the parking brake shoes. Stripping everything down and re-assembling, cleaning and re-greasing as you go does wonders.
As for the squeak in your steering this is often a bearing or joint needing some lubrication, it's possible the mechanic driving it into the garage heard it and spent a minute applying grease while he/she was under the car, or noticed an issue that was quick and simple to fix and just did it for you without noting it on the work sheet.