I've watched the video and yes he does mumble the dreaded N word, as he was saying it he realised he shouldn't be? He recited a nursery rhyme which he was taught in his youth, it came up to the N word automatically, like it probably does with millions of other Britons of a certain age, you have to mentally substitute a word for it. As another poster has said when we were younger the term the "paki shop" was common, we also had one which was referred to locally as the "nig-nogs". As a child I knew no better and in the 70's that was the norm, not right but it was still the norm. I grew up with a half-caste half sister in a non-racist Irish family yet these terms were still used by my parents.
Oh and personally I can't stand Clarkson and Top Gear.