It doesn't, except in so far as wild ones [like wild anything else] probably won't be white or piebald. If most of the UK ones are dark, it would be too much to expect they are of wild origin, more probably selectively bred to look a bit more like the 'real thing'. Incidentally, there is at least one small herd of white Yaks in private ownership in the UK.
There seem to be two main colour strains in Zoos- black, like these and at Whipsnade, or White and/or 'Roan- the latter coloured a bit like Dairy Shorthorn cattle. I haven't seen any of the roan ones in the UK but they are in European zoos.
In the Himalayas there may be other colours too, I don't know. Some of the 'pack' yaks you see in TV documentaries have white heads/faces and tails too
There are 4 main strains of domestic Yaks. You have the standard black yaks, with grey noses. This is the most common type. There is the Imperial, very similar to the black, but instead of having a grey nose, their nose is black. The final two common strains are Trim, and Royal. Trim yaks are black with small white markings on their heads, feet, bellies and tails. The royal yaks are the piebald animals. They can be almost entirely white or almost entirely black, with anything in-between. If anyone is interested I could explain how to breed for these strains and what the crosses will be.