Fealty and forelock tugging to the class above you and passive aggressively restricting the freedoms of the class below you is as much a part of British culture as the single digit amendments to the constitution.
Changing it would be like changing the language to French.
The UK has a constitution, just not one that is codified in a single written document with a special privileged status. (In practice, there is also a lot more to the US constitution than what’s written down in the document referred to as ‘The Constitution’.)
Changing it would be like changing the language to French.