The fingering system is called "Albert System" or "Simple System." Most modern clarinets use the Boehm/Klose system. That doesn't mean the horn is "bad" or anything.
I am not sufficiently well versed in vintage clarinets to determine the manufacturer by the two pics you've posted. Are there any identifying marks on the horn? Any info as to how you acquired it? Note that there are sometimes stamps under one of the larger key touches and those could be helpful.
I mentioned Albert System fingerings. That could mean fairly old. That could mean that it uses an old intonation standard called "high pitch." That means that your horn will not play in tune, no matter what you do to it. That means you should check to see if there's a stamp that says "LP," "L," "H," or "HP." That means that you won't be able to play in tune with any modern instrument. That means that the value of the horn would be $0. That would be a shame. "That" was used way too often in this paragraph, and that's the truth.
I also can't really tell if this is an A, Bb, or C clarinet. It's a little hard to tell, even if you have an exact measurement.
You can probably get this horn repaired, but the question of low pitch or high pitch should be determined first. You might have to sink a few dollars into it to get the horn in some condition to tell. You don't want to spend hundreds of dollars to find out that you can't play it anywhere. It's also possible that the horn is 100+ years old, as the Albert System has been around for a while. A collector could be interested, but you'd have to see if you can find some info as to which company produced it.
Thank you so very much for this excellent and comprehensive reply - very helpful. Sadly there were no identifying marks anywhere. We've ended up selling the clarinet to a collector who knows about restoring old horns so hopefully it will be played again, even if it's on its own.