Choreography may be the most difficult of all performing-art forms. The dance-lover is all too aware that the standard theatre or opera repertoires contain thousands of works. Dance, by contrast, has a repertoire that numbers only in the hundreds, and most companies commonly draw on only dozens of works.

For England’s three largest ballet companies to produce new pieces within months of each other, therefore, is unusual. That the works come from four of the most artistically acclaimed choreogr...