Yep, British plugs all have replaceable cartridge fuses from 3 Amps (700 Watts) to 13 Amps (3000 Watts) depending on the power of the appliance. Appliances beyond those ratings are generally hardwired or a special plug is sometimes used. British plugs are used in many countries around the world, including Ireland, Cyprus, Singapore, Hong Kong and many counties in Africa and the Middle East, but those countries generally use the branch circuit as in the US.
In the UK, the ring circuit is often used. This means the cable doesn't terminate, as it would in a branch circuit, but actually goes back to the panel, meaning both ends of the cable are connected to the breaker. This means thinner cable can be used, as the current flows both ways and the circuit breaker for general socket circuits is normally 32-Amp 230-Volt, 7400 Watts. An American branch circuit of 120-Volt 15 or 20 Amps gives 1800 or 2400 Watts. So overloading should be less likely on the British system -- unless all the load is at one extreme end of the circuit, or if there is a break at one end of the circuit, or if an unfused 2-way plug adapter is used to connect two 13-Amp appliances through a single 13-Amp socket, none of which would be detected by the circuit breaker.
Here in Spain, the German plug (no fuse) was adopted decades ago (similar to French but totally different to both the Italian and the Swiss for example) and traditional Spanish sockets (which used to have fuses) are rarely seen now. We have 16-Amp sockets, 16-Amp circuits connected to 16-Amp breakers, meaning each outlet can supply the circuit's maximum of 3680 Watts. In the UK, 16-Amp socket branch circuits are sometimes used, too. I am interested in electrical systems in the UK, USA and Spain. They all have their pros and cons regarding safety and convenience.