A search for squarks and gluinos in final states containing jets, missing transverse momentum and no electrons or muons is presented. The data were recorded by the ATLAS experiment in s=7TeV proton–proton collisions at the Large Hadron Collider. No excess above the Standard Model background expectation was observed in 35pb−1 of analysed data. Gluino masses below 500 GeV are excluded at the 95% confidence level in simplified models containing only squarks of the first two generations, a gluino octet and a massless neutralino. The exclusion increases to 870 GeV for equal mass squarks and gluinos. In MSUGRA/CMSSM models with tanβ=3, A0=0 and μ>0, squarks and gluinos of equal mass are excluded below 775 GeV. These are the most stringent limits to date.