You probably don't need +-6V, +-5V will do.
The transformer isn't a 1:1, it must be a 10:1 to get 24V from 240V.
That relay is rated at 12V so it probably won't activate unless it's powerd by more than about 9V, use a 6V relay.
I don't see any reason why you can't generate the +-V supply from the 24V supply on your transformer. The circuits attached will work, the first uses zenners and can supply about 30mA, so it might not work for your relay uses more than 8mA, the second uses regulator ICs. You could also use bufferd zenners, like the one in your 3V supply, but you'll need a PNP trnasistor for the negitivce supply.