This is a simple Gamma mode hot air engine. This example was made by Davies Charlton but the same engine was also made by at least one other maker.
The engine has a displacement cylinder and power cylinder mounted parallel to each other, with connecting rods connected to a common crankshaft. The hot end of the displacement cylinder is metallic and heated by a small, single wick meths burner. The burner and hot end are surrounded by a metal shroud for draft proofing. The cold end is fitted with cooling fins.
The power cylinder is mounted on the other side of the metal frame, through which the connection is made between the two (providing nominal heat exchange/storage). The crankshaft has two flywheels, each with a crank pin for the two pistons.
As bought, it was not working. This was probably caused by oil residue in the cylinders. A thorough clean out fixed it.