The ECHR is an international agreement like many, many others. It has special status in UK law only because we chose to: that was the purpose of the Human Rights Act. You can also take complaints of breach to the European Court of Human Rights, but they have no enforcement powers (in particular, Russia often decided not to bother complying, and we've avoided enforcing their ruling on prisoner voting rights with their tacit consent).

It used to be the case that we were also tied into the ECHR (and playing nice with the rulings of the ECtHR) because it's required by EU law even though it's not an EU instrument and the ECtHR isn't an EU court. But as we've left that's no longer an issue.

Finally, I'd just say that there's little objectionable about the Convention, and for the most part it tracks very closely with existing British common law (not surprisingly, as it was a Churchill-supported project in the first place and intended to export what was great about the British tradition of liberty as much as to bind us into Europe). There are a few edge cases where politicians and certain newspapers get into enormous flaps about individual cases, but it's really not that constraining a convention: most of the clauses have get-outs for crime, morality and public order and the margin of appreciation is generally quite broad. It's not perfect any more than, say, the Canadian Charter of Rights and Freedoms is, but the complaints are mostly grandstanding.