Incitement to racial hatred is a specific offence under various sections of the Public Order Act 1986, which replaces and extends similar provisions in the Public Order Act 1936 and the Race Relations Act 1965, but supplements and does not replace the old common law relating to breach of the peace. Note that a prosecution under any of these sections requires the consent of the Attorney-General.
Public Order Act 1986 s.18
(1) A person who uses threatening, abusive or insulting words or behaviour, or displays any written material which is threatening, abusive or insulting, is guilty of an offence if he intends thereby to stir up racial hatred, or having regard to all the circumstances, racial hatred is likely to be stirred up thereby.
(2) An offence under this section may be committed in a public or a private place, except [entirely inside a dwelling].
Public Order Act 1986 s.19(1)
A person who publishes or distributes written material which is threatening, abusive or insulting is guilty of an offence if he intends thereby to stir up racial hatred, or having regard to all the circumstances, racial hatred is likely to be stirred up thereby.
Public Order Act 1986 s.23(1)
A person who has in his possession written material [or sound or video recordings] which are threatening abusive or insulting, with a view to publication or display, is guilty of an offence if he intends thereby to stir up racial hatred, or having regard to all the circumstances, racial hatred is likely to be stirred up thereby.
R v Malik  1 All ER 582, CA
A Black Muslim D made a speech lasting about an hour, in which he described white people as vicious and nasty, referred to them as "white monkeys", and said that any white man who laid hands on a black woman should be killed. He was convicted of inciting racial hatred and imprisoned for twelve months; the Court of Appeal affirmed the conviction and the sentence.
R v Relf (1979) 1 Cr App R (S) 111, CA
D produced and distributed a flysheet Jungle News, which portrayed black people as closely related to apes, stated or implied that they were all violent criminals and/or scroungers, and made extensive use of words like "nigger" and "wog". He was convicted of inciting racial hatred contrary to s.5A of the Public Order Act 1936 and sentenced to fifteen months' imprisonment, reduced to nine months' on appeal. Lawton LJ said there was no proof that D's conduct had led to violence so far, but the constant repetition of lies might in the end lead some people to believe them, and a custodial sentence was entirely appropriate.
R v Birdwood (1994) unreported, Judge Pownall QC
The Dowager Lady Birdwood, aged 80, was convicted of possessing and distributing anti-Semitic literature; this was in breach of a conditional discharge for a similar offence two years earlier, and she was given a suspended prison sentence.
In March 1997, three members of the violent neo-Nazi group Combat 18 were jailed for between 12 and 17 months under s.23(1). They were found in possessions of magazines and other materials that included bomb-making instructions and "hit lists". Judge Pownall QC told the defendants no one would deny their freedom of speech, but all freedoms have responsibilities to go with them. Their freedom was to speak as strongly as they wished; their responsibility was to do that without being threatening, abusive or insulting.
Note also the specific offence of taking part in chanting of a racialist nature at a designated football match, defined in the Football (Offences) Act 1991.
Before the 1997 election, the Labour Party proposed the creation of an offence punishable with imprisonment for any person to deny that millions of Jews were systematically murdered by the Nazis during the period 1933-45. Such an offence already exists in a number of European countries, and the European Commission is in favour of its extension throughout Europe. While the activities of neo-Nazis rightly give cause for concern, it is arguable that this response would create an even more dangerous precedent, reminiscent of Stalinist policies in the USSR when only the "official" version of history was lawful and any alternative version led to imprisonment. Nothing more has been heard of this proposal since the election.