Sources of inherently cold electrons extracted from laser cooled atoms have the potential to transform electron imaging. These sources promise both the spatial coherence and high current required for picosecond molecular scale imaging. Here we demonstrate arbitrary and real-time control of electron bunch shape and thus realise a major step towards alleviation of electron source brightness limitations due to Coulomb explosion. We describe the spatial coherence properties of a cold atom electron source in the framework of a quasihomogeneous wavefield. The model is used as the basis for direct measurements of the transverse spatial coherence length of electron bunches extracted from a cold atom electron source. The coherence length is determined from the measured visibility of a propagated electron distribution with a sinusoidal profile of variable spatial frequency. The electron distribution was controlled via the intensity profile of an atomic excitation laser beam patterned with a spatial light modulator. We measure a lower limit to the coherence length at the source of l_c = 7.8 +/- 0.9 nm.