I already have wireless network infrastructure and an internet connection. I also live in an old house with very thick walls... I haven't checked GPS reception indoors here, but if it's anything like mobile phone coverage there will be little to zero reception, and it's far too much effort to run in a cable for an exterior antenna.

Also, just having a quick look I can't see anywhere locally that sells GPS synchronised wall clocks (or at least analogue-style ones, which is what I want)

It was a good suggestion though, thank you. I had not though of NTP alternatives. I did look at radio-controlled clock as well, but there's no public broadcaster of sync signals in Australia. Apparently you can DIY it [1] by playing the signal over headphones and have the RCC pick it up as harmonic leakage from the cable, but that would not look good with a wall-mounted clock.

[1] http://www.jrcomputing.com.au/Set_Watch/Set_Watch_Auto.html