The Communications Act Section 127 was based on the existing Malicious Communications Act (1988) passed by the Thatcher government. And the UK has had plenty of other speech restrictions like blasphemy laws (abolished by Blair) to suspiciously broad offences against obscenity existing since time immemorial.

The Online Safety Bill is the brainchild of a Conservative government, included as a flagship commitment in a Conservative manifesto aiming to appeal to conservatively minded voters, a successor administration to the Conservative government who brought us the national porn block. Nothing makes it easier for such legislation to be passed more than revisionist nonsense about how the wonders of negative liberty meant we never needed any of the positive protections this law specifically supersedes and it's all the left's fault anyway.

Even prior to the Human Rights Act the UK was bound by Article 10 of the EChHR, it just wasn't directly enforceable by UK courts (one first had to exhaust domestic legal challenges and then bring a case in Strasbourg at the ECtHR)