The biggest single costs of any speaker is the woodwork followed by veneered finishes. A budget sub isn't going to have a fancy finish, so that leaves us with woodwork. In order for the speaker to stop and start cleanly then the cabinet must be robust and solidly braced. That's just not possible for such a small amount of money, even with volume economics and Chinese manufacturing helping. The best you'll get is a box that sounds a little hollow when you rap on it with your knuckles. This means that the box will sing along with the driver. That's okay if you just want boom and rumble, but not what you want for accuracy.
For deep bass that stops and starts cleanly you need a big driver or a medium sized long throw driver and couple it with an amp that can control the cone supremely well. Those are expensive things to achieve.
Finally, for Hi-Fi use then you'll need an amp with high level inputs. The additional cost of the electronics has to come from somewhere.
These plus shipping and import costs, marketing costs, distribution margins, warranty support costs, manufacturer's profit, taxes and the rest is why the numbers just don't stack up.
For £100 secondhand you'll probably be looking at travelling to go pick up some old Paradigm stuff (PDR8) or Jamo (Sub 200), or Acoustic Energy (Aegis Evo Compact) or Wharfdale (SW150), maybe a old REL Storm, or god forbid some piece of cheap Eltax. The point is all of these subs were built for movies rather than music. So it didn't matter about precision just as long as they did deep and loud. You're looking for something altogether more sophisticated: a sub that does well for music. Straight away you're looking at subs that on average cost £500+ new, and they're not going to come up secondhand for £100 unless there's something wrong with them. That then leaves the new generation mini-subs such as the MJ Acoustics Pro 50 MKI. These hit the market at £300-£400 and undercut the traditional music/movie subs. That means they were very popular when new and also very popular in the used market too. As a result they hold their value well.
In short, unless you drop lucky on someone selling a high-end sub without realising its value then I think you should either be prepared to accept an AV sub or revise your budget up quite a bit to get the proper thing.