Data recorded at centre-of-mass energies up to 209 GeV by the OPAL Collaboration at LEP2 are analysed to search for signatures predicted by models of low scale quantum gravity in extra spatial dimensions (LSG). The measured cross-sections and angular distributions of the process e+e- -> W+W- are compared to the expectations of the Standard Model (SM) and LSG theories. No significant deviation from the SM is found and constraints are derived on the mass scale, MS, of LSG models. The results are combined with other OPAL limits from e+ e- -> e+e-, mu+ mu-, tau+ tau-, gamma gamma and ZZ production.