Re: DIY Electricians
First, your appliances will work just fine if you swap Live/Neutral. However, your fuses (or circuit breakers) and switches won't be as effective, so you will be unsafe. Long explanation:
The Neutral and Earth wires are connected together somewhere. In the UK, this is often at the connection point where the wire to your house ends, just before your electricity meter. In that case the electricity supplier will have lots of places where their combined neutral/earth wire is connected to metal rods in the ground.
So, if you accidentally touch the Live wire in your home, the power will flow from the electricity supplier's Live wire, through you, through the ground, through those metal rods, and back through the electricity supplier's Neutral wire. There will be a fuse in your fusebox and/or in the plug, on the Live wire, which will blow, stopping the current, and limiting the electric shock you get (although it can still kill you).
If you have Live/Neutral reversed at the fusebox, then the fuses are effectively on the Neutral wire. So when you touch the wire that is labelled Neutral, but is actually Live, the fuses won't help you. The power will stay on and you may keep frying.
In the case of a short-circuit that's just Live-Earth, not going through a human: The fuses are designed to protect against wires melting and things catching on fire, but they won't do that if they're in the Neutral wire. This may cause your house to burn down.
Also, if you turn a light off to change the bulb, or pull a fuse to do electrical work on a circuit, then you're safe - that turns off the Live wire, and if you accidentally touch the Neutral it won't matter. If you have Live/Neutral reversed at the fusebox, then the switch is effectively on the Neutral wire and if you touch Live then it may kill you.