Definition 1: Modal music is one that uses a modal scale other than the Ionian mode (major scale), Aeolian mode (natural minor), melodic minor and harmonic minor scales common in the music of the classical period. Under this definition, Thomas Tallis' Third Mode Melody, which inspired Vaughan Williams' composition of Fantasia, is modal because it used a Church mode, namely, the Phrygian mode. The Third Mode Melody (
http://www.youtube.com/watch?v=tXt-2BmgVbA) known to us today is not the original but Vaughan's rearrangement, which is underlined by traditional tonality despite having sprinkles of modal coloration here and there.
Definition 2: On top of using a non-classical mode, modal music is one that focuses chiefly on melodic beauty inherent from the mode, in contrast to classical music that focuses on harmonic progression and heavily gravitates toward a central triad with a clear sense of "major" or "minor". Vaughan Williams' "The Lark Ascending" (
http://www.youtube.com/watch?v=HWwBh0dzgi4&feature=related) is an example of modal music. It sounds "oriental" (e..g, A Chinese traditional music:
http://www.youtube.com/watch?v=hN5k6WtYvso) for I see the image of Yuna Kim, not a British skater.
Although church music (e.g., William Byrd and Thomas Tallis) in Elizabethan era employed church modes (a borrowing from foreign sources), I don't know if they have been used in street music as well. And the Hexatonic scale used in The Weaver and the Factory Maid is different from those church modes, so I'm not sure about its connection to Elizabethan music, either.
But I think you proved a point: "English" music does not always sound Germanic. Since the early Britons contained mainly Germanic tribes such as Angles, Saxons, Jutes and Danes, I naturally consider English folk songs that carry Germanic elements to be the "real" ones. Of course, it is a stereotype, biased against Normans and other peoples that have contributed to the establishment of the Kingdom of Great Britain.