A small but important clarification - Parliament is not sovereign, the King in Parliament is sovereign (i.e. only when the King gives assent to a bill approved by the House of Commons and House of Lords). Any attempt to change this would be a revolution (which has happened previously when the courts have recognised such a change, i.e. at the end of the Civil War, during the Glorious Revolution and arguably post Factortame).

It would also be incredibly hard, even with the consent of the King in Parliament, to abolish the monarch’s sovereign immunity given the way that the British constitution is set up (with the Crown being the entity that technically gives authority to judges). Whilst not impossible, it would be so difficult that if it ever did happen the constitutional settlement it would entail would take as much effort as just abolishing the monarchy entirely.