My 5D3 was sourced from Europe and had a 12 month Canon warranty plus an additional two years third party warranty on top of that, still with the huge savings on price. I have heard that things may have changed on terms of where the cameras originate, which might mean the Canon warranty is not available, although you will still get three years in any case. The best thing to do would be to contact them and confirm the facts.
With all that said, in my experience all that Canon UK requires in order to honour warranty in the UK is a "proof of purchase" for which a UK VAT receipt ought to be sufficient. For some reason the advice is to ask for one when you place the order. I asked as suggested and I received a copy. So far, almost a year later, I have had no need to put any warranty cover to the test for my camera.