In the US, the Fifth Amendment of the Constitution says the government cannot take private property for public use without providing just compensation. I don't know whether any similar right exists in the UK.
The U.K. does not have a proper written constitution, nor a real bill of rights. It does have the European Convention on Human Rights, but that was passed by an Act of Parliament and can be withdrawn by another Act of Parliament, and in fact the Conservative Party keeps proposing just that.
There are no limits on parliamentary sovereignty, which is what the US Founding Fathers fixed with the US Constitution, but even that was the second attempt, after the failure of the Articles of Confederation, and the Bill of Rights came after the Constitution itself, which is why it is formed of amendments.
