It used to be the case that UK jazz musicians were important - from the beginning of the 60s onwards especially - in setting the stage for a "Europeanisation" of jazz and especially the evolutions of fusion and free improv. So, on the one hand, musicians like Dave Holland and John McLaughlin were sucked over to NY by Miles Davis, and labels like ECM included the generation around Kenny Wheeler, John Surman and so on as mainstays.
Similarly in the mid 80s, it is without doubt that one can take bands such as Loose Tubes and Jazz Warriors as trailblazers for a new moving on of the jazz.
Over time, British musicians have continued to be in demand to bring their knowledge internationally.
Now however, there is a new trend afoot, which is akin to "technology transfer". More and more young musicians are realising their potential through taking advantage of UK educators, both in UK (but also abroad).
Abroad, the new main influences are John Taylor, for many years in Cologne, and now Django Bates, for the past few years in Copenhagen and now teaching in Bern(e) for part of each month. Django's Stormchaser band shows his influence, and it's even the case for bands now performing at 12 Points in Porto, such as Berlin's Schneeweiss and Rosenrot, where I know that Johanna Borchert and Peter Eldh are Copenhagen graduates.
The other important development is the number of European musicians who have taken advantage of the education and performance scene over here. Some of them are now in the forefront of their respective scenes. For example, Stian Westerhus, the whizz kid of Norway, is a graduate of Middlesex University, Robin Fincker (now back in France) was at the Royal Academy of Music, Ingrid Laubrock, now the toast of the improv scene, was at Guildhall ( I think) and of course lived here for over a decade, Froy Aagre studied at Birmingham. Hans Koller is still here, of course, but does his main work for the big bands in Germany (especially NDR). Emilia Martensson - still with us in London - is Swedish and studied at Guildhall. Jasper Hoiby is Danish and still here too. I haven't done a thorough trawl but I think that gives the gist?
It was most recently brought home to me by my recent conversations with Rory Simmons about Eye of a Blue Dog, which involves Elizabeth Nygaard (Norwegian but still here) and Terje Evensen, who is Norwegian but studied at Trinity.
While it is getting harder to have gigs abroad for UK musicians who, because of the dire international funding system, are often treated as second class and unheard, our musical influence is permeating through in another way!
However, as Jack Davies has pointed out in his blog the cost of study is getting higher and higher. So that may put off these foreigners coming here. So another window on the world for British jazz will be shut.