Does the British Bill of Rights ensure equality citizens?

There is no British equivalent to the US Bill of Rights. The closest analogue is the Human Rights Act (HRA) of 1998, which incorporates the European Convention on Human Rights into domestic law. The HRA does not explicitly guarantee equality, but it does prohibit discrimination on various grounds, including race, sex, and disability. However, the HRA is not a constitutional document and can be amended by Parliament at any time, unlike the US Constitution.