Well there is the English guitar, a different animal from the Spanish variety, with a different tuning (CEGCEG), but that has passed into history.Historically the pipes and the fiddle have been the dominant folk instrument, but that applies equally to all our neighbours.The concertina and the Northumbrian pipes are the nearest things we've got to specifically English instruments, though whether that makes them suitable to be the national instrument is another question.
Personally, I would nominate the spoons, enlivener of many a dull session when the old guy in the corner starts flailing away to the annoyance of the earnest folkies who have come to practise their polkas glumly.