On the BS546 sockets, the 2A types were genrally used as lighting outlets, and were sometimes controlled by a wall switch.
15A types were fitted where a full 3kW load might be needed, and in the typical house there would have been only one per room, generally next to the fireplace for an electric heater. Cooker control units could also have a 15A outlet, and in many kitchens that might have been the only
The 5A types were then pretty much general-purpose for all smaller appliances, and maybe multiple 5A outlets in a room.
Here's Table A.2 which Kenny referred to:
As you can see from the associated rule A.25, for compliance with the Regs. there should have been no more than three 5A sockets on a 15A circuit, but in practice I think that was widely ignored. I certainly remember seeing old places in which there were dozens of 5A sockets on a 15A branch cct. Given the diversity of use and the fact that most were for convenience and for light loads (radios, electric blankets, etc.). I doubt that was much of a problem unless taken to extremes.