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The UK has literally never had free speech. America fought a war over this. I’m not sure why you’re confused by their actions here.

Part 1 sounds like that but Part 2 is doing the real work.

UK Human Rights Act 1998

1 Everyone has the right to freedom of expression. This right shall include freedom to hold opinions and to receive and impart information and ideas without interference by public authority and regardless of frontiers. This Article shall not prevent States [EU states - the UK is still under the ECHR] from requiring the licensing of broadcasting, television or cinema enterprises.

2 The exercise of these freedoms, since it carries with it duties and responsibilities, may be subject to such formalities, conditions, restrictions or penalties as are prescribed by law and are necessary in a democratic society, in the interests of national security, territorial integrity or public safety, for the prevention of disorder or crime, for the protection of health or morals, for the protection of the reputation or rights of others, for preventing the disclosure of information received in confidence, or for maintaining the authority and impartiality of the judiciary.