> the British public found their posts offensive
For any given piece of speech, it's not hard to find someone who's offended by it. So that's a terrible standard for free speech rules, unless you want to have a country of silence.
> You've read into the article a problem that doesn't exist
You may have a point. Let's examine the examples:
1. The airport bombing comment is probably the easiest to call unprotected speech. Even on first reading of the article, I thought "That sounds like an actual threat...Let's see what else they have."
2. The comment about the soldiers could also be considered a physical threat, but it's more of a stretch; "I hope X dies and goes to hell" isn't nearly as strong as "I'm going to kill X".
3. I can't find the specific wording of the comment regarding the murdered children.
4. That leaves us with the poppy-burning; but it seems like this would be a clear case of protected speech in the US.
That's a grand total of one correctly classified instances of unprotected speech (1), one incorrectly classified instance of protected speech (4), and two for which the correct classification is unknown or shaky (2-3). That is, if you take "correct" to be "protected speech according to US law," which is the only classification of protected-vs-unprotected speech I'm familiar enough with to do this analysis.
The data indicate that the UK might have a systematic problem correctly classifying instances of protected speech, but you're right; that certainly isn't a clear-cut conclusion from the article.