According to this Guardian quiz, the British monarch is not required to have a passport. The question asks "Which of these things does the Queen not need to have?" and gives the options: "A driver's licence", "A licence plate on vehicles", and "A passport". The correct answer is:
All of the above That's £75.50 saved every few years not having to renew a passport for a start. The Queen learnt to drive in the military in the 1940s but is not formally required to have a licence, and is able to drive in unmarked vehicles
I can understand the first two since both a driver's licence and vehicle licence plates are internal state matters and a state can decide to do whatever it wants with them. However, a passport, while also issued by a state, is a document that is required by other states to let you travel.
The official site of the British Royal Family states that:
As a British passport is issued in the name of Her Majesty, it is unnecessary for The Queen to possess one. All other members of the Royal Family, including The Duke of Edinburgh and The Prince of Wales, have passports.
That's all well and good, but I don't understand how the UK can waive the requirement here. Surely it is up to the country the monarch is traveling to to decide whether or not they have the required documents to be allowed entry. So is this actually true, does the Queen of the UK not require a passport and, if so, what's the legal basis for it? Can't another country refuse her entry for lack of a passport or is there some sort of global law/regulation that allows any head of state to travel without the proper documentation?