Debian Squeeze and raspbmc both work fine, so I'm happy it's not a power or SD card issue.
I've tried reflashing the SD card, but the problem remains. I will try another SD card to make sure the problem's not there, but the card was working fine with Sqeeze on it.
I am using one of these HDMI > VGA adaptors http://www.amazon.co.uk/gp/product/B007KEIRNG, so that might have something to do with it, but the problem only affects Wheezy.
Anyone got any ideas?