I think may be someone should point out the realities of the British constitution.
The house of Lords has very limited power. Legislation is passed to them and they can propose amendments but at the end of the process the final version is whatever the house of commons says it is. Their effective power is to delay and to propose sensible changes (which they do). However, the house of lords is strictly speaking the supreme court (but see below)
However, the Monarch has considerable power which, by convention, is not used. The Queen effectively appoints the government by selecting the Prime Minister who then selects other ministers. Only the Queen's nominated government has the right to propose legislation. Once legislation has been passed it doesn't count until it has received "Royal Assent". So - quite a lot of power. Also the star chamber - officially appointed by the queen but like everything else following convention - can effectively rule by proclamation. The Queen is also commander in chief of the armed forces, final arbiter of the legal system. The main limit on power is the inability to do certain things without legislation which must be passed by the house of commons. Dating back to the restoration after the English civil war all British tax legislation is limited to one year and without the consent of parliament all taxes lapse. That is the real limit on the "official" power of the English Monarchy.