Not really. Since what you're calling for specifically is the Monarch to start blocking bills: it was established in the Bill of Rights Act 1689 (which would form part of the basis of a constitution if codified) that Parliament is sovereign, and the actual Sovereign can only act on the advice of parliament apart from when exercising royal prerogative, which is done on the advice of ministers.
One example of royal prerogative is proroguing parliament, which we've discussed. Another would be giving, or not, Royal Assent to a bill. The last time Royal Assent was refused was in 1708: https://en.wikipedia.org/wiki/Scottish_Militia_Bill and that was also on the advice of ministers, as they'd changed their mind about a law that had completed its passage through parliament.
In other words, what you're asking for has not happened in over 300 years.