Police Volunteer?
The ancient weapon has to be designated to be used on a regular basis as a weapon, not necessarily in the military.
If a mad man happens to visit a museum, grabs a medieval battle axe on display and starts butchering other visitors, this wouldn’t qualify.
I think it’s that they don’t want to issue something heavy like an assault rifle or Uzi to volunteers, but at the same time think that they’ll be more comfortable with a rifle than with a pistol or a shotgun. Hence, the M-1, a rifle with the strength of a pistol.
Do they have to re-hire the canons each morning? Or is it just a ceremonial firing? Could they fire a dean, instead?
B-52 are still in use and they haven’t made any new ones since the '60[sup]s[/sup]. I think some of our 155mm. field pieces are from the Korean War era. Although they both will have had new electronics upgrades since they were made.
Not in use today, but the Turks cast the Dardanelles Gun in 1467 and shot it at the British in 1807.
The 1911 was used officially by the US Army from WW1 all the way through Desert Storm. I think they have moved on to a 9mm pistol (they wanted to fire standard NATO 9mm Parabellum which is used by many other countries), but you can still get new civilian-market 1911’s and someone must be buying them. It’s not so old, but the M1 Garand is still around. I used to know a guy who had a few in his basement. The AK-47 (1947) is still used extensively in the Middle East and in Communist and formerly Communist lands.
Rather like the Browning .50 the Oerlikon 20mm cannon is 70+ years old and still widely used.
I’d say, offhand, that BUFFs are a serious contender for the title. Some of them have airframes dating from the 1950s and are intended to continue serving until around 2040, and they are unquestionably “weapons.” (I just read somewhere that there are third-generation pilots and crew serving on their grandfather’s craft, with a fourth generation in the - par’n the pun - wings.)
The other class that occurs to me are naval and Marine swords. Many have been handed down from prior generations and I believe some currently being carried are of Revolutionary War vintage. Many date to ca. 1900. Yes, they’re 99.99% ceremonial, but they’re still weapons, many have probably inflicted casualties, and you won’t catch me telling a full-dress jarhead his sword is a decoration. 
The Swiss Guard (Vatican police) still train with pikes & swords (and carry them when they are in official dress). Presumably they’d use them, if attacked.
Are fists not weapons?
If they don’t count, then I would say a club.
That’s a good one! One could also guess that the actual swords and pikes are ancient.
Not completely fitting the OP (as modern-use weapons wouldn’t be actual antiques), but…police side-handled batons are modeled after the Okinawan Tonfa, which is a centuries-old design at least.
Bagpipes.
Thou art a sneaky person who knows his British law.
Just to re-clarify, we’re looking for weapons that were originally manufactured long ago where the originals are still in use today.
We’re not looking for weapon designs as that quickly becomes fists, rocks, knives, etc. which is fairly obvious and uninteresting.
Yes, Mishmar Ezrahi/Civil Guard.
I remember using the Martini Henry during a display at Cardiff castle. Apparently a theatre company had closed down and they still had a load of them in storage as props, the army was contacted and they were taken into custody - and they date back to the 1880’s.
Certainly gave an authentic feel to our mock battle of Rourke’s drift.
“Nobody told ya’ to stop working.”
It’s not used as a weapon, but the 9 O’Clock Gun was cast in 1816 and is still fired daily.