Regulation of advertising can indirectly become a free speech issue if it reflects a particular bias in society, which is what O'Neill tries to establish, saying that it reflects a larger drive to ban politically incorrect speech. He might have a convincing argument there, but uses a rather stupid example: an add that made a pun on the word 'faggot'.

Sorry, but the word is offensive, certainly in a society that criminalised homosexuality and regularly locked up gays up to forty years ago. I get the point that minorities should not be oversensitive, but pejoratives that are derogatory towards a (still disadvantaged) minority simply are harmful.

Asking them to be banned from advertising is entirely reasonable.

The main reason O'Neill has decided to be offended by regulation of advertising is that the authority in Britain has decided to restrict advertising of 'junk' food during children's programmes. He uses various fallacies in arguing against this, such as stating that children today are healthier than they were in 1900. I'm sure they are, but that doesn't mean that fast food is good for them.

He also says that advertising only has an impact on only 2% of all children's eating decisions. I don't know how significant that is or isn't. But if advertising doesn't work, why do companies advertise?

One answer to the question what effects advertising has could be that it creates a large enough amount of demand to pay for it. Another answer is that the demand for a product is more or less fixed, but the allocation of the demand between several producers is flexible and can be influenced by adverising. In the first case, regulation of harmful products is justified. In the second case, it does no harm and may even improve competition in the industry.

Either way, the public wins.