That's the version of the 'Fireside Socket' that fits a standard 2g box. The original had a non-standard square footprint and was sold under the 'New Day' brand, the owner of which had a patent on the swing-out fuseholder that was inherently touch-proof.
Would that be standard socket on the left handside then the fuse to protect the round pin outlets on the right, say via a 5 or 3 amp fuse?
Yes. They are 2A sockets, which would normally be fused at 5A at the CU for fault protection only. So a 5A fuse would be fitted in the fireside socket instead.
Is that around the introduction of the square pins, so you had sockets that took old and new for a while?
It was actually a bit later, although round-pin sockets remained in widespread use for decades after the 1947 introduction of the 13A. There had been six different round pin sizes as they tended to be matched to the application, because appliances didn't move around as much in those days. If you had a 5A 3-pin socket for the standard lamp and a 2A 2-pin for the radio, it didn't matter if the radio always sat on the sideboard and the standard lamp always stood by the armchair.
The idea of the Fireside socket was to feed an electric heater and two small appliances such as a standard lamp and a radio. Triple unfused points were never permitted, so it gave you an extra point in the same space without any more wiring. Of course, it totally defeated the idea of all plugs being interchangeable in all sockets, which we have come to expect but was rather a novelty then. I think it was more of a solution to a problem that didn't exist.
If you have any spare of those, I would be very interested in an example or two for the museum. We have two of the square ones in mint unused condition, IIRC one badged 'New Day' and one with the name ground out of the mould, but not the 2G one badged MEM.