This paper describes a search for the Standard Model Higgs boson using $\rm e^+e^-$ collision data, with centre-of-mass energies between 192~GeV and 209~GeV, collected by the OPAL detector at LEP. The consistency of the data with the background-only hypothesis and various Higgs boson mass hypotheses is examined. A lower bound is obtained on the Higgs boson mass at the 95\% confidence level. At higher masses, the data are consistent with both the background and the signal-plus-background hypotheses.