I just got off the phone to Xiaomi UK and they said that their phones have a 2 year warranty on them if you buy from the following;
Xiaomi store (Online / Westfield)
Currys PC World
Mobile Phones Direct
If you buy from eBay it won't get the 2 year warranty. I'd assume you'd still be able to get the warranty if you bought second hand as long as you could validate proof of purchase, i.e get the original reciept.