Catalysis of the reaction: (2E)-4-hydroxy-3-methylbut-2-enyl diphosphate + 2 H+ + H2O + oxidized  = 2-C-methyl-D-erythritol 2,4-cyclic diphosphate + reduced .
(E)-4-hydroxy-3-methylbut-2-enyl diphosphate synthase activity