Nationality & the British Regimental System

[Raellus]

A preliminary Google search hasn't turned up a definitive answer, so I thought I'd ask the question here.

Does one have to be a particular nationality to join one of the non-English regiments in the British Army? In other words, does one have to be Welsh to serve in the Welsh Guards, Scottish to join the Scots Guards, etc.? Conversely, can a non-member of a particular British nationality join its national regiment? If I'm using incorrect terminology, please feel free to correct me.

Wikipedia indicates that the Scots Guards recruit Scots, but can non-Scots join as well? Wikipedia also claims that the two Irish regiments in the Irish Army recruit in Northern Ireland (and also accept Irish nationals). Neither article holds that the respective regiments do not accept Brits of other nationalities.

Do all or most members of a particular British nationality (e.g. Welsh) who wish to serve in the British Army join their national regiment, or do they join/are assigned to whichever regiment the army wishes them to? In other words, do they have a choice, or is the choice made for them? Last question, how common is it for army personnel to transfer from one regiment to another?

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