"I have heard it described as wanting people to play music from their tradition, ..."

Phew! For a moment there I thought we were going to get into (yet another) endless, sterile, nit-picking debate about what constitutes one's own tradition. Luckily Jim came to the rescue with his statement that:

"Basically it was Britons performing British material at first, though the suggestion that they used their own accents rather than say 'oirish' or 'Mummerset'"

That's probably all you need to know.

Although to keep this in perspective, it's also worth recalling that the 'proscription policy' applied to a particular club, at a particular time (50 years ago!) - a club which had specific objectives and formulated a policy which helped it to meet those objectives.