In case the Conservative Party in particular and the press in general have forgotten, we already have a Bill of Rights. It was passed in 1689 and embodies the Declaration of Rights, 1688. Admittedly is was only England (and Wales) as it was before the Act of Union but a quick amendment would sort that out.
It is also worth mentioning that the US Bill of Rights was not drafted as a comprehensive statement of the rights of citizens, but is just a nickname for the first 10 amendments to the constitution; things they forgot the first time around.