Hi Fernando,
Indeed the Peterson book brought up the kings head marks and basket hilts in America, as was of course well established in his book on arms in Colonial America. That reference along with George Nuemann's book on swords of the American Revolution carried the scope of European arms in this country quite well.
The article you mention by Barthorp, is that the Osprey reference?
In any case, in the development of the Scottish basket hilt itself, as I have understood, especially through the extensive work by the late Claude Blair, the developed basket hilt did evolve from the Continent. It does seem that influence came to British shores quite early in English swords (i.e. examples found on the wreck of the Mary Rose), but that primary influence on the Scottish hilts came from dusagge (cf. Sinclair sabres) of mostly northern Europe. These heavy basket hilt sabres were impressive to the Scots who served in these regions as mercenaries, and began evolving into the well known Scottish forms around 16th century. There is a good deal of confusion on just how much cross diffusion between the developing Scottish forms and English examples, but the characters began taking on certain distinctions independently.
With these basket hilt forms which seem to have expatriated to France as described earlier, it was not a developmental move, but more a geopolitical transference. It does seem that more fully developed guards in hilts were present in other countries some time after the Scottish and English hilts evolved in Britain, but they seem likely independent of these and quite likely from the same root with the closed guard dusagges.
That is what I have understood and recall from researches on these years ago, and I hope it makes sense. These are incredibly fascinating swords, and another of my addictions (along with cup hilts !
)
All the best
Jim