Results are presented of a search for particles decaying into final states with significant missing transverse momentum and exactly two identical flavour leptons (e, mu) of opposite charge in root s = 7 TeV collisions at the Large Hadron Collider. This channel is particularly sensitive to supersymmetric particle cascade decays producing flavour correlated lepton pairs. Flavour uncorrelated backgrounds are subtracted using a sample of opposite flavour lepton pair events. Observation of an excess beyond Standard Model expectations following this subtraction procedure would offer one of the best routes to measuring the masses of supersymmetric particles. In a data sample corresponding to an integrated luminosity of 35 pb(-1) no such excess is observed. Model-independent limits are set on the contribution to these final states from supersymmetry and are used to exclude regions of a phenomenological supersymmetric parameter space.