That’s clearly nonsense. You not protected from the indirect or non-governmental consequences of your free speech in the UK or Europe, just as much as the US. You can lose your job or suffer other social consequences from exercising your free of expression. In fact there are a whole raft of unofficial-ish ways to control free speech in those countries (like this and that) that don’t cross the line into outright criminalization of free speech.
But that’s in addition to the actual explicit legal infringements discussed in this thread. The UK Constitution doesn’t protect you from social consequences of exercising your right to free speech and doesn’t protect you from being sent to prison for exercising your right to free speech (by say calling the PM a coconut, or saying nice things about ISIS or Palestine Action). The US Constitution doesn’t protect you from social consequences of exercising your right to free speech but does protect you from going to prison for exercising your right to free speech. So it is objectively better at protecting free speech.
Finding a rando on the Internet who says differently isn’t an argument against this fact, even if the rando in question works at a university, and puts their claims in an authoritative sounding numbered list form. I can find a very authoritative sounding numbered list that claims the prequel trilogy are the best star wars films, it doesn’t make it so.