If your generator is plugged into their own circuit, it wouldn't change much.

If you plug it into an overloaded ring final (which is not uncommon in the UK - half our house's sockets are on a single ring), you have to rely on the generator being able to detect faults to protect that circuit.

You could also overload that circuit's wiring. If you have a a 16A Ecoflow, plug it into a 32A ring, you could draw 48A before tripping the grid circuit breaker, potentially causing significant heat in the wires. Dinky 3A generators won't do that but I don't think they're the limit our government are talking about.