We study the parameter space of the constrained exceptional supersymmetric standard model (cE 6 SSM) consistent with a Higgs signal near 125 GeV and the LHC searches for squarks, gluinos and Z . The cE 6 SSM parameter space consistent with correct electroweak symmetry breaking, is represented by scans in the (m 0 , M 1/2 ) plane for fixed Z mass and tan β, with squark, gluino and Higgs masses plotted as contours in this plane. We find that a 125 GeV Higgs mass only arises for a sufficiently large Z mass, mostly above current limits, and for particular regions of squark and gluino masses corresponding to multi-TeV squark masses, but with lighter gluinos typically within reach of the LHC 8 TeV or forthcoming 14 TeV runs. Successful dark matter relic abundance may be achieved over all the parameter space, assuming a bino-like LSP with a nearby heavier inert Higgsino doublet and decoupled inert singlinos, resulting in conventional gluino decay signatures.A set of typical benchmark points with a Higgs near 125 GeV is provided which exemplifies these features.