It seems that there's sufficient concern around dog meat that some people want the UK to ban its consumption.
I'm unclear what could justify singling out dogs in particular. If the UK really is a nation of animal lovers, then I'd have thought more people would be vegetarian - but, even then, I'm not sure it would be legitimate for the state to ban the consumption of meat.
But to argue for a ban on dog meat, while happily eating pigs, cows, etc, seems hypocritical.
J. S. Mill argued that, if Muslims were a majority, they would have no right to ban the eating of pork, simply because they find it abhorrent. The same seems to apply, mutatis mutandis, to dog meat.
Edit: see also this later post on US measures.