Let $ L $ be a lattice ordered effect algebra. We prove that the lattice uniformities on $ L $ which makes $ \ominus $ and $ \oplus $ uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete effect algebra associated to $ L. $ As a consequence, we obtain decomposition theorems - such as Lebesgue and Hewitt-Yosida decompositions - and control theorems - such as Bartle-Dunford-Schwartz and Rybakov theorems - for modular measures on $ L. $