A lot of the ads on
are for kitten- and puppy-farms, people running unlicensed businesses selling animals, which is against the law. As far as private sales is concerned, as much as I'd like to see it stopped, I think that's legal. (I'd be delighted to be corrected on this point.)
If
know that some of their adverts are illegal (and they ought to know by now) they must take reasonable steps to stop them, otherwise they too will be breaking the law by allowing it. The easiest way for them to rectify the situation would be to introduce a "no livestock" rule. It's worked elsewhere on the internet.