Funny that you should mention the system in what was then Great Britain; the Constitution of the modern U.K. and its antecedents in English law are very much part of a live constitutional crisis in the question of the power of the executive versus the power of the legislature.

The ruling below contains in it an extremely fair overview of some of the issues you mischaracterize in your last paragraph. I think it's understandable that you got it wrong; comparative constitutional law is not an especially popular thing, and there are further reasons I'll return to below.

Two of the most senior judges (by rank) in the UK and likely the most highly regarded (by the legal profession generally) public law judge, wrote this ruling that was handed down Thursday. The judges are also justices of the Supreme Court of the United Kingdom, which will hear the appeal, although nobody seriously expects that the UKSC will overturn the judgment unless the parties agree to ask the Court for permission to consider some matters listed in the judgment as "common ground" as in dispute. The parties are the national executive (through a head of the new department for exiting the European Union) and a mechanism which allows public interest cases to be brought against the government by concerned citizens and residents; several individuals are effectively the true claimants.

I'm going to make references to several numbered paragraphs in the ruling, which you can read in full here. Unfortunately the source-text-with-markups version is not yet online, but that will follow in due course as is general practice. The parties agreed that drafts of the rulings would not be made in advance because of the risk of leaks that might harm either party's interests, and that they would agree to a true copy that would go online first, so that there could be no question about the exact wording of the ruling, because the matter was (and is still) virtually certain to be considered by the Supreme Court in December.

https://www.judiciary.gov.uk/wp-content/uploads/2016/11/judg...

The judicial review of executive authority is not novel; this judgment refers (at paragraphs 26, 27, and 28) to case law established in the 17th century.

Just prior to the American Revolution the "Intolerable Acts" complaints made frequent reference to the English Bill of Rights (1688) and most of the American leadership made it abundantly clear before the Revolution began that the unrest was founded in their desire to protect their rights as Englishmen.

What was eroding their rights was not the monarch (again, this was established in the civil wars of the 17th century, and the Glorious Revolution (judgment, para. 26)) but factional politics in the British Parliament. Rival factions were vying for power, and the largest groups coalesced around Frederick North and Charles James Fox. The former was strongly supported in the countryside by rich land owners (with their wealth being generated by tenant farmers) and professionals, merchants, and other cityfolk in the urban centres of the day. As is common even today, the "country" party was highly conservative both socially and economically, while the "city" party was keen on progressive reforms to governance, extension of the franchise, and -- crucially -- equity for Englishmen living outside England. The economic conservatives were trying to preserve the balance of accounts available to the government in the ongoing war with France and its allies and a few other parties (the Seven Years War, which in U.S. history lessons tends to be called the French & Indian War) and were hostile to spending money garrisoning the western frontier of the colonies unless paid for locally, and they were thus intractably opposed by interests in the colonies that favoured expansion Westward into the river valleys that had been won from France, but knew there would be violent opposition by the people already living there who had been France's allies.

The Foxite Whigs were very close with many Americans, especially Benjamin Franklin, and were keen on breaking deadlocks in the British parliament on this and other common matters. They essentially propagandized against the Northites' insistence that the elected legislatures in each of the colonies was the appropriate venue for discussing grievances and raising petitions to the North-led government, with Charles James Fox himself proposing a system whereby Englishmen living in the colonies could elect Members of Parliament directly without owning land directly in metropolitan Britain and without being physically present to cast a ballot. The Northites were intractably opposed to this, as the Colonies would almost certainly provide the Fox faction and its allies a clear and possibly even huge majority in the House of Commons.

The only way the King was involved at all is that he stupidly -- or perhaps because of the porphyria which clouded his mental faculties from time to time, sometimes seriously enough that he went through periods of being called "mad" -- was playing favourites in pressing North to choose personal friends to head up government departments. He even more foolishly pressured North to formally recommend the appointment of a handful of his favourite courtiers as (mostly, but not wholly, ceremonial) colonial governors.

However, that was essentially a Revolution-enabling error of judgment: Fox and Franklin exchanged letters agreeing that because enough non-Englishmen were living in the colonies, and had moved there to escape actual tyranny by properly absolute monarchists -- especially in the German states -- they should caricature the conflict as between Colonists and the King rather than political factions jostling in the elected House of Commons, and engage them as allies in the escalating political conflict, especially as outright armed rebellion seemed likely. (There was of course a substantial history of armed rebellions just prior to the English Civil War, and riots and other civil disturbances in London in economic downturns as the one caused by the expense of the Seven Years' War and preparing for the likely resumption of hostilities with France, Spain and the Dutch Republic).

George III was also the monarch of a German state (Hannover), and that was used to further convince immigrants -- especially German ones -- to support the Revolution. The North government's decision to hire mercenaries from Hesse-Kassel and other German states rather than draw down on reserves of British soldiers -- it was essentially a cost-saving measure, and was quietly opposed by the King because it significantly enriched German princes that were in competition with his family's interests -- played right into that characterization. (cf. Franklin's 1777 work, "The Sale of the Hessians").

So, the "sovereign" was at the time Parliament, and it was too factionalized to protect itself from challenges in the courts, and that somewhat stayed the hand of the North government -- and especially George Germain and the Earl of Sandwich, who were the government officials in charge of dealing with the rebellion in the Thirteen Colonies. However, it did in 1773-1774 make it even more difficult to bring a lawsuit in a court against the government, so to some extent you are right that 'sovereign immunity' was in play, although not especially successfully. Had open warfare not broken out, it is very likely that the North government would still have collapsed (resulting in a series of uneasy coalition governments), that the Court of Appeal would have held that the ex parte cases for relief against the British executive were in fact valid (the British government mostly defaulted, deliberately, on several court actions brought by Americans).

Additionally, one of the live constitutional issues -- especially in Massachusetts -- was the primacy and authority of the executive of Britain backed by the British parliament over the legislative assemblies of the colonies. The Northites and their country-conservative allies were already losing ground, with Parliament taking powers from the British executive and delivering them to executive councils and legislative councils i many colonies, starting with the Québec Act (1774).

Essentially the American Revolution was triggered by ineptitutes and reactionary decisions taken by a weak proto-Tory government in a very divided Parliament during a brief pause in a world war and in a period where trans-Atlantic trade in raw materials was crucial to their pressing economic needs. (By 1780, the British were again in active warfare, and without allies, against five European powers, with fighting on four continents; they chose to stop fighting in the American Revolution rather than risk losing possessions elsewhere, especially the sugar and rubber plantations they controlled and were fighting to protect from the Spanish and Dutch).

It was the failure of a government which barely controlled the elected House of Commons, and yet was unable to bring itself to share power - even temporarily and tactically - with other factions both in England and in the English colonies.