From Wikipedia: United Kingdom citizens have a negative right to freedom of expression under the common law.[98] In 1998, the United Kingdom incorporated the European Convention, and the guarantee of freedom of expression it contains in Article 10, into its domestic law under the Human Rights Act. However there is a broad sweep of exceptions including threatening, abusive or insulting words or behavior intending or likely to cause harassment, alarm or distress or cause a breach of the peace (which has been used to prohibit racist speech targeted at individuals),[99][100][101] sending another any article which is indecent or grossly offensive with an intent to cause distress or anxiety (which has been used to prohibit speech of a racist or anti-religious nature),[102][103][104] incitement,[105] incitement to racial hatred,[106] incitement to religious hatred, incitement to terrorism including encouragement of terrorism and dissemination of terrorist publications,[105][107] glorifying terrorism,[108][109][110] collection or possession of a document or record containing information likely to be of use to a terrorist,[111][112] treason including compassing or imagining the death of the monarch or advocating for the abolition of the monarchy (which cannot be successfully prosecuted),[113][114][115][116][117] sedition,[114] obscenity,[118] indecency including corruption of public morals and outraging public decency,[119] defamation,[120] prior restraint, restrictions on court reporting including names of victims and evidence and prejudicing or interfering with court proceedings,[121][122] prohibition of post-trial interviews with jurors,[122] scandalising the court by criticising or murmuring judges,[122][123] time, manner, and place restrictions,[124] harassment, privileged communications, trade secrets, classified material, copyright, patents, military conduct, and limitations on commercial speech such as advertising.

UK laws on defamation are among the strictest in the western world, imposing a high burden of proof on the defendant. However, the Education (No. 2) Act 1986 guarantees freedom of speech (within institutions of further education and institutions of higher education) as long as it is within the law (see section 43 of the Education (No. 2) Act 1986[125]). UK defamation law may have recently experienced a considerable liberalising effect as a result of the ruling in Jameel v Wall Street Journal in October 2006. A ruling of the House of Lords—the then highest court of appeal—revived the so-called Reynolds Defence, in which journalism undertaken in the public interest shall enjoy a complete defence against a libel suit. Conditions for the defence include the right of reply for potential claimants, and that the balance of the piece was fair in view of what the writer knew at the time. The ruling removed the awkward—and hitherto binding—conditions of being able to describe the publisher as being under a duty to publish the material and the public as having a definite interest in receiving it. The original House of Lords judgment in Reynolds was unclear and held 3–2; whereas Jameel was unanimous and resounding. Lord Hoffman's words, in particular, for how the judge at first instance had applied Reynolds so narrowly, were very harsh. Hoffman LJ made seven references to Eady J, none of them favorable. He twice described his thinking as unrealistic and compared his language to "the jargon of the old Soviet Union."<br abp="587">

"Recently there have been a spate of free speech controversies, from Phil Robertson’s temporary suspension from Duck Dynasty for comments made on homosexuality and race, to the resignation of Firefox CEO Brandon Eich over a political donation made six years ago in support of traditional marriage, to the revocation of an honorary degree and cancellation of a commencement speech to be delivered by human rights activist and Muslim apostate Hirsi Ali at Brandeis University for critical statements on Islam."
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None of those things have anything to do with freedom of speech because the government was never involved in any of them. It is not possible for a non-government entity to infringe on anyone's freedom of speech, because censorship is an action which does not qualify as infringement or a violation of constitutional rights unless it is preformed by the government.

That said, it is rather appalling that freedom of speech in the U.K. is so severely limited. I can't believe you can actually get arrested for saying the wrong thing. Makes me glad we've got a Bill of Rights here. Even if it does often get trampled on, at least we have it.