" I have heard it described as wanting people to play music from their tradition,"
Basically it was Britons performing British material at first, though the suggestion that they used their own accents rather than say 'oirish' or 'Mummerset'
The policy was to concentrate on the British repertoire that had been made available through The BBC 1950-54 collecting project.
On one of my first visits to Ewan and Peggy's home to copy their tapes they gave me access to half a dozen tapes from the Beeb collection and suggested that if I wanted to expand my small repertoire there was plenty there to choose from.
Peggy also had about ten folders in the filing cabinet, of songs in alphabetical order she had typed out for their own research - they were for the benefit of anybody who came to the house to work.
she had made multiple copies of each and the last of each was marked 'final copy' so she could replace it as they ran out.   
We still have typed Xeroxed copies of about a dozen songs I took away around 1968.
As I've said, when Lomax first came to Britain Ewan and Bert and virtually everybody else on the scene was singing American songs, largely recorded by The Library of Congress - Lomax tore a strip off them for "neglecting their own tradition".
Both Ewan and Bert took his point and ,as far as I'm concerned, the policy worked and loads of people started singing British material - a great help in this was the ten-series Caedmon series of albums, 'Folk Songs of Britain' (Lomax was instrumental in getting this produced); it was later released on the British label, Topic.
On Ewan's 70th birthday he was given a symposium in London - Pat and I were there when Alan and Ewan sat in front of an audience and discussed the beginning of the revival - this was one of the points covered.
There was no objection to taking say Irish, Scots or American song of British origin and singing them in your own accent - I have a couple of dozen Scots songs in my repertoire, lots of Irish and a couple of American ones - I've had to work on them to fit my Scouse-ish accent - just added 4 Scots onesa and one America one (Hedy West's 'Fair Rosamund', which I almost osmosised from hearing Peggy sing it so often).
Eventually it was not so much about national origin as accent - once we started work in the Critics Group analysing and relating to the songs we found that they just didn't work in an accent that wasn't your own.
Ewan and Peggy actually did a Folkways album entitled 'Two-Way-Trip', swapping British and America versions of songs - in my opinion, it was their least successful album - neither managed to pull the accents of for the choruses - they never did it again, to my knowledge.
Said this before but, much of the animosity Ewan felt towards Dylan was based on a fear that, having pushed British songs to the fore, Ewan worried that the situation would revert back to as it was pre-Lomax.
When I first got involved at the beginning of the sixties, the scene was swimming with Joanie clones and Dylan doublers - I found clubs like The Wayfarers in Manchester and the occasional trips to the Singers a bit of an oasis.
Sorry about the arguments - it won't happen again if I can help it.
Jim Carroll