British household electrical systems are normally built as one large ring circuit, originally in order to save copper after WW2.
This means you don't have breakers for each branch circuit (there are no branch circuits), just the single mains breaker for the house. This single breaker is too large to trip from a short from occuring in the smaller wires inside an appliance.
So each plug (or hardwired device) needs it's own dedicated smaller fuse instead.
Houses built post-1960s (with more than one floor) will have more than one socket ring each protected by a circuit breaker at the distribution board, usually one per floor for general sockets, with a separate one for the kitchen, and usually individual 32A breakers for things like electric ovens and hobs.
Lighting rings are also separate, usually on 6A breakers. We cheap out on cable by not running neutrals to the switches, which causes nerds headaches when they want to install generic smart light switches.
My house is reasonably large (worked hard, all my own money) and has a 20-way distribution board with separate socket and light rings for groups of rooms. It’s handy for isolation purposes.
More recent builds’ rings will be protected by a combination of MCBs and RCDs, or individual RCBOs (now the cost has come down) which combine the two functions and is ultimately the safest option for most situations.
Individually fusing plugs (and in the case of high-draw appliances like washing machines and dryers, protecting with a fused socket) is still a very good idea. And don’t get me started on earthing practices in other countries…
To add: Many pre-90s buildings don’t even have circuit breakers, they have fuse boxes with fuse wire (different fuse to the one being talked about). Literally just a piece of wire that burns out at a certain current and breaks the connection. You “reset” it by putting a new piece of wire in.
The second fuse at the plug allows using a narrower gauge of wire in the device’s cord. Let’s say you have a lamp with a 3A fuse, the cord only needs to be able to handle 3A, so then it can be lighter and cheaper. If it had to handle the same amperage as the circuit it’s plugged into then it would be seriously impractical and expensive.
Of course there are modern ways of solving this but fuses are dirt cheap and already implemented.
My last place had a 1970s Wylex board, which at least had plug-in MCB modules that replaced the fuse wire holders and can be reset. However given you can still buy fuse wire in DIY stores there still must be installations out there that need it. Shudder.
I recently replaced the old fusewire plugs with MCB modules. Really didn't fancy trying to wind a bit of wire around the terminals in the cellar in the dark :)
This means you don't have breakers for each branch circuit (there are no branch circuits), just the single mains breaker for the house. This single breaker is too large to trip from a short from occuring in the smaller wires inside an appliance.
So each plug (or hardwired device) needs it's own dedicated smaller fuse instead.