Nigel, so to be clear? Your Euro 240v 3 pin plug home electrical wall socket service is actually 2 hots and 1 neutral, and NOT 1 hot, 1 neutral, and 1 separate ground, as it is here in the States? We call your type of service here as, 220v single phase power.How would 0 to V+ be the same as V- to 0 to V+?, obviously it's only half. And assuming 240V mains, the output of a half wave rectifier is 120V RMS.
And it's not changing the mains (unless you have a high current draw on it), it's simply changing what appears on the output of the diode.
Historically TV's used half wave rectifiers, but after a while the electricity companies insisted that they used full wave ones - back in the old two pin plug days it didn't matter, it was random choice if a TV used the positive half cycle, or the negative one, so it balanced out. But once 13A 3 pin plugs were in universal use the VAST majority of TV's were running off the positive half cycles, leaving the negative half cycles unused - and this created a negative bias on the electrical system which the electrical companies didn't like