Woodcock's only surviving compositions are a set of twelve concertos (3 for flute, 3 for recorder, and 3 for oboe) published by Walsh and Hare in London circa 1727. The concertos were originally published under the title: XII Concertos in Eight Parts, the first three for Violins and one small Flute, the second three for Violins and two small Flutes, the third three for Violins & one German Flute, and the three last for Violins & one Hoboy. The proper Flute being nam'd to each Concerto. The three flute concertos in this set are the earliest known published for that instrument, and the three oboe concertos are the first known by an English composer. Vivaldi published his opus 10 flute concertos shortly thereafter, in c.1728, and the earliest oboe concertos were published by the Italian composer Albinoni in 1715.