Bussey-type air pistol
With thanks to Dave. He says:
I've measured the calibre at 6,3mm.
Length is 253 mm or as near as 10"
Weight is 7.5 ozs or 214gms.
Using a fairly weighty pellet (26.9gns) it chronos at a heady 0.2ftlbs. That was the best result from a string of 3.
On seeing this, John Griffiths, author of The Encyclopedia of Spring Air Pistols, said:
On looking closer at the shape of the gun and the mention of a piston, I think it is a true airgun. It must be a take on the Bussey pistol... The artwork on the box is reminiscent of the Giffard brochures, and I would guess it dates from a similar period...
It is quite a bit shorter than the Bussey (length about 38cm).
Dave also supplied this pic, confirming it was a spring piston pistol:
Later, John posted:
I could not find a picture of the original auction lot I mentioned previously, but found a listing, which says that Lot 608 was in the sale of the gun collection of a Monsieur A.C., and described as “Lot 608. The Aero-Baliste pistol, with instructions for use and original box”.
I also found an Italian auction (Czerny) mention where one was sold, but some reason only the box is pictured and no gun. This time the box is wood. The sale was on May 10, 2019. We can assume it is the same pistol from the description. However the overall length is a bit different to yours, so presumably it had a longer barrel.