Protection of life and freedom against arbitrary decisions in the UK date back to the Magna Carta (1215, with the version currently "on the books" in England dating to 1295), the Petition of Rights (1628), the Habeas Corpus Act of (1679), and the Bill of Rights and Claim of Rights (1689), which combined set out the foundation for ensuring fair trials and protections against punishment without trials etc. (and which are reflected in large part in current US law as well...). In the intervening centuries there has been a number of acts adding to these rights.
In addition, by passing the European Communities Act (1972), the UK parliament made EU law supreme to UK law in a number of areas, which means that the EU human rights legislation is binding, providing additional rights.
If anything, the complexity of UK constitutional law in the form of those (and many other) acts, principles and court judgements makes it harder for government to just change things, as the UK court are loathe to let parliament get away with that kind of thing unless they have made pretty damn sure to dot all their i's and that what they try to do is not inconsistent with other laws or principles (in which case they'd have to revoke or replace those as well to get their way with the courts).
Governments have tried "simply decreeing" more than once, and had the courts tell them they are simply wrong. Specificially, they've been told several times that what they've tried to do is in violation of EU law, and thanks to the European Communities Act, they can't override EU law.
After passing that act the situation has become quite complex, as there are some legal scholars that argue that this act actually limited parliamentary sovereignty, and that the UK parliament thus can't actually just revoke it, and revoking it would be the only way for the government to take away any rights guaranteed in the European Charter of Human Rights (revoking it would also mean leaving the EU).
If the courts agree with that assessment, then barring the EU itself revoking the charter the government would not have a legal way of modifying those rights in any way other than adding to them.
Now, there are many things lacking in the UK constitution, and I agree that having it in a clear, written form would make things easier (and at the very least make people more likely to be aware of what rights they actually have), but the situation is quite a lot better than what most people complaining about (lack of) rights in the UK think it is.