It is not really visually attractive, like some other mechanical devices may be. However, the way it functions is rather neat, and it is in fact a joy to turn the handle and see (and hear) the coins rushing through the machine. The machine seems to be from the 1960's or 1970's.
Turning the handle on the right spins the disc, which forces the coins (through centrifugal force) through a height adjustable gap (checking the thickness of the coins), under a rubber wheel which forces the coins through an opening between a slider and a kind of cog wheel with 5 circle-section cut-outs in which the coins fit (see photo below). The coins can not pass without turning the wheel one fifth, but the wheel can not turn more than that either.

The coins then are deflected downwards, into whatever bag or tube you want to fill with it. The number of coins can be read on the counter, or course. How many coins you want inside the bag can be adjusted using the handle on the front, either 20, 24, 40, 50, 100 or 200 coins in one bag. The cog wheel mentioned earlier is blocked when this number of coins is reached, so you can fit a new bag. Pressing the same lever downwards, unblocks it, and the next bag can be filled.

New coins can be fed into the machine either directly on the rotating disc, or from the cover, which is designed to receive coins and feed them in such a way into the machine that it is not over-filled.

The company Metra West does not exist anymore, neither does it have any patents to it's name.

I found a much older machine, produced by the Neue Geldzählmaschinen Fabrik (NGZ) in Berlin, Germany. I'm not sure how old it is, but the person who was selling it, thought it might be from the 1940s. This one is made of cast aluminum with a vintage grey hammerite paint finish.

The machine functions exactly the same as the British one. Though NGZ holds patents for a whole range of machines to handle, count, stack or deliver coins, I could not find a patent for this machine, so it must have been an invention by somebody else.

The company NGZ still exists, and had their last patent on counting coins granted only a few years ago. That one can count all sizes of coins at one time.