According to the legal encyclopedia, Halsbury's Laws of England, members of the Royal Household cannot be arrested in civil proceedings.
The encyclopedia states that arrests cannot take place in the presence of the monarch - so as long as they stay by the Queen's side, they can't be cuffed by a police officer.
This rule also applies to the various royal palaces across Britain, such as Buckingham Palace and Kensington Palace.
If a royal is anywhere near a palace, they cannot be taken into police custody
One royal has been given a criminal conviction.
https://www.chroniclelive.co.uk/news/uk-news/places-members-royal-family-cant-15695419