I would have to nominate Vaughan Williams for that laurel - given his influences, predominantly English Tudor polyphony and (especially) traditional folk song.
There are plenty of others who come close (such as RVW's chum Gerald Finzi, English-born but of a Sephardic Jewish Italian heritage), and then there's another of his mates, Herbert Howells. RVW's closest friend Holst has already been mentioned. (Not very fun fact: Howells, Holst and RVW were all from Gloucestershire). But RVW claims the prize hands down, surely.
HH correctly points out that Elgar's musical toolkit was basically German (think Brahms), something equally true (or even more so) of two great composers thought of as quintessentially English, Parry (wrote a 'Cambridge' Symphony, an 'English' Symphony and of course the tune for Jerusalem) and Stanford (though he was born in Ireland). Much of RVW's work, especially in the early period was modal, built as it was on modal tunes as found in folk song. It became so much a part of hs musical vocabulary that he could effortlessly write original tunes that sound like folk song even though they're actually not. (The central section of The Lark Ascending being a case in point).