Check whether your LG washing machine actually uses any hot water. I found quite by accident that our Indesit doesn't use the hot feed on 40C or 60C washes - I discussed it with the repair man (who fixed a pin-holed pressure sensor). He said it's quite normal for modern washing machines only to use the hot feed when the was is over 60C - so as my washes are rarely over 40C, my hotfill is cosmetic!
Our older (10 yrs?) Bosch has hot and cold fill and definitely draws on the hot water for a 40C wash. Haven't checked for a 30C wash. Shame the pipe is so long that it is only just getting warm by the time it fills the washing machine, so I guess we'd be better off with cold fill only.
In the new house, the washing machine should only be a couple of feet from the thermal store, so the problem will disappear.