I'm guessing that the car is an ex demo so they didn't bother filling in the service book etc until now !!

The third year warranty will be provided by the dealer and not ARUK so you'll have to take them on their word but personally I'd get it confirmed in writing from them !!

As to whether you should be worried... well that all depends on which dealer you're buying it from !!

IMO if it's one that based in West London then you'll be fine... if it's one based in another part of London then I hope for your sake they don't have the attitude that some of their other franchises have

(I hear that they don't though

)