The issue is it is very unclear what Nikon or canon will do. They almost certainly don't adhere to any warranty so at best you have to pay for the repair or send it back to HK. However,there have been a number of cases where they have refused any kind of repair even at cost unless a valid UK receipt was presented.
It is all a bit of a gamble, but at bets you end up with a camera with a similar warranty to a second hand camera, but you pay more typically.
There is also a it difference between Nikon and canon. Canon seem more lenient and are more likely to repair grey imports, Nikon are very strict. Even then there are differences between regions, e.g. EU law forces Nikon to provide some kind of warranty even to grey market goods under certain conditions, but in USA and Australia Nikon will tell you to get lost if you can't show proper receipt of origin form within the region.
Again the scaremongering all the big grey importers offer their own warranty with local repair which is much better than buying second hand from that perspective and as said a I had a repair carried out by a canon authorised centre without any issue. If you need a valid UK receipt surely that rules out second hand kit being repaired as well as I've never received any original receipts except for my flash.