The equation of state and the crystal structure of the gillespite-structured phase Ba0.5Sr0.5CuSi4O10 have been determined at seventeen pressures, ambient to 6.5 GPa, using powder neutron diffraction. At ~4.45 GPa, a structural phase transition is observed from the low-pressure structure, in space group P4/ncc, to a high-pressure structure in space group P4212. No experimental evidence was found for the presence of weak superlattice reflections with wave vector (2π/3a, 2π/3a, 0) that have recently been observed in the high-pressure, single-crystal X-ray diffraction patterns of the isostructural compounds BaCuSi4O10 and BaCrSi4O10, and it should be noted that the possibility remains that the crystal structure reported here may represent the average of a similar commensurately ordered phase. The isothermal bulk modulus of the low-pressure phase, determined using a third-order Birch-Murnaghan equation of state, is 81.6(8) GPa with an initial pressure derivative of −3.3(3). The bulk modulus of the high-pressure phase was found to be smaller, estimated as 59.4 GPa. The phase transition appears to be driven by the need to relax the strong over-bonding of the alkaline-earth site, but apparently not that associated with the square-planar copper sites, which remain significantly over-bonded in the high-pressure phase. The phase transition equates to the loss of the centres of symmetry in the low-pressure phase, and results in marked differences in the tilting of the symmetry-independent Si2O7 polyhedral groups, and in the aplanarity of the associated bonded CuO4 square-planar groups. From the limited data that exists on isostructural compounds of gillespite, the low-pressure structure appears to be unstable at volume reductions of 4–6 %, however the structure of the high-pressure phase seems to depend on whether or not the cation in the square-planar site is a Jahn-Teller ion.