Sorry prcscct I didnt separate the last bit well
The difference between Thailand and the UK is that Thailand has a written constitution (which it seems to have changed about 37 times since it went to a constitutional monarchy in the early 20thC). The UK has an "unwritten" constitution, one that is termed a constitution of "Statute and Law" - the legal code is the constitution.
The Bill of Rights 1689 set the stage, detailing the way things were ran and the individual rights of citizens, etc. It predated the US constitution by roughly 100 years and is supposedly an influence in that later document. The BoR1689 has since been surplanted by statutes and laws that expand on it in separate Acts and Statutes.
For example the BoR1689 permits landowners and gentlemen to carry sufficient arms to protect themselves and their property. We got rid of those rights bit by bit as we realised that carrying weapons meant people got killed, gun improvements made that easier, and it was written in a time when there was
no police force. The yanks prefer to kill each other with gleeful disreguard for Common Sense (spot the sly Thomas Paine ref????) and keep a 250 year old law on the books despite the fact they aint carrying muzzle loading one shot muskets any more. You'd have thought the word "Ammendment" might have given them the clue it could be changed, but they also seem to not understand what the "well regulated militia" bit refers to either.
The UK also has an older primary legal system called the Common Law. Common Law is an amalgam of Danelaw from the North and Anglo Saxon laws from the South. The Common Law is only superceded by Statute (or "Admiralty") Law - Acts of Parliament, local and revenue statute, etc. Thailand doesnt have, to my knowledge, such a secondary system.
The constitutional monarchies run under much the same rules as far as I understand. All Acts of parliament and political appointments must (on paper) have royal consent that could theoretically be withheld. I think Thailand based its constitutional monarchy rules on those of the UK.
The only difference I can see easily if that the Queen is nominally the head of the Church of England as well as ruler, wheras the King of Thailand doesnt nominally run the Buddhist religion in Thailand.
The reason our democracy sort of works and Thailands is sort of a mess is IMHO just down to the fact we have been at it for longer. Thailand has been democratic for less than 100 years, we have been democratic since the Parliamentary Protectorate/Commonwealth period 300 years earlier..... so I cut em some slack on not understanding what it means and how it works. On being too thick and xenophobic to look and learn from their "elders" I dont.

"Science flew men to the moon. Religion flew men into buildings."
"To sin by silence makes cowards of men."