Given the historical development of the Sovereign as the ‘Fount of Justice’, civil and criminal proceedings cannot be taken against the Sovereign as a person under UK law. Acts of Parliament do not apply to The Queen in her personal capacity unless they are expressly stated to do so.
However, The Queen is careful to ensure that all her activities in her personal capacity are carried out in strict accordance with the law.
Under the Crown Proceedings Act (1947), civil proceedings can be taken against the Crown in its public capacity (this usually means proceedings against government departments and agencies, as the elected Government governs in The Queen’s name).
In the case of European Union law, laws are enforced in the United Kingdom through the United Kingdom’s national courts. There is therefore no machinery by which European law can be applied to The Queen in her personal capacity.
However, it makes no difference that there is no such mechanism, as The Queen will in any event scrupulously observe the requirements of EU law.
As a national of the United Kingdom, The Queen is a citizen of the European Union, but that in no way affects her prerogatives and responsibilities as the Sovereign.
https://www.royal.gov.uk/MonarchUK/Queenandthelaw/HowUKandEUlawaffectTheQueen.aspx
So the law does not apply to the queen, even EU law as they would be applied through UK courts.