If you are thinking of the pug giving the nazi salute thing, there are a number of qualifications worth adding to that:

- The judge expressed pretty much surprise that the defense did not even try to raise a human rights defense, and that as a result he could not take that into account in his judgement. It came very close to the judge basically telling him that his defense were idiots and that he'd have likely gotten off if they'd argued it was a human rights violation to go after him for this.

- The law in question is awful. To the point where the Crown Prosecution Service has drawn up a number of guidelines for prosecution that means very few people actually ends up prosecuted because there are many easy outs. Firstly, what you get prosecuted for is to cause something grossly offensive to be published to someone likely to take offense electronically, not for telling an offensive joke. There are exemptions that protects broadcasters quite substantially. These two factors exclude most potential cases. The CPS guidelines also takes into account, and advises against prosecution, if the poster of the material takes it down or otherwise acts to limit distribution, and apologize, once made aware it has caused offense.

- He was not prosecuted for making a simple joke. He was prosecuted for bookending a video with the joke wherein the bulk of the video itself is him repeating 'gas the jews' and 'sieg heil' over and over dozens of times interspersed with Hitlers speeches. The intent of the law is to stop hate speech. The reason he got into trouble is because it was not at all obvious that the intent of his "joke video" was to make a joke and not to use a mildly funny joke as an excuse to get away with spreading hate speech. The intent of the law would be entirely gutted if you could just insert a slightly jokey context around a bunch of hate speech and claim it was just a tasteless joke (we can certainly argue whether stopping that hate speech is justified). You'll note that none of the "reporting" on it that reproduces enough of the video to show the joke have faced prosecution, because it takes that very specific small amount of bookending of a lengthy section of hate speech without any kind of contextualizing to emphasise the joke aspect to step over the line.

This makes it very different from "just" making offensive jokes. An example there is that complaints about Jo Brand recently suggesting the people throwing milkshakes at far right politicians might try acid instead went nowhere because she contextualized it in a way that made it very clear she did not actually want anyone to go out and do it or take it seriously. And she didn't repeat "throw acid at Farage" over and over in the middle of it.

- The person in question did not take it down after he was made aware. After it blew up, he conducted interviews where he explicitly expressed that he understood that it had been grossly offensive. He basically admitted to the offense in the media, at great length, giving the judge pretty much no choice.

Despite the above, he got close to the mildest reaction possible, with a small fine.

To reiterate: The law in question is awful, but the "nazi pug" affair is a horrible demonstration of why.

> then you don’t believe in freedom of speech.

It is not binary. No country on the planet allows unabridged freedom of speech. Including the US. Because everyone recognizes that speech have effects, and some of those effects have significant implications that causes very direct harm. Other times the problem is not the speech, but how and where it is conducted - speech that is fine in private may be seen very differently if you shout it in someones face. As such a lot of restrictions on speech are not restrictions on you actually saying what you want, but trying to strike a balance to prevent the way you express yourself to cause unreasonable harms to others.

Now, I agree that the UK doesn't get the balance right on that.

But I also do not believe anyone who claim to want to restrictions on speech, because in my experience that just means they have not thought through the consequences. In practice, once you start walking through examples, I've yet to meet someone who will not get to a point where they agree some things should be limited. They may try to suggest it's not actually a restriction on speech, though. But most regulation of speech is not about what you can say, but about how and where you can say it, in recognition that what is "just speech" to one person can be an outright assault or serious harassment or incitement to violence to another.