A new scalar resonance, called the radion, with couplings to fermions and bosons similar to those of the Higgs boson, is predicted in the framework of Randall-Sundrum models, proposed solutions to the hierarchy problem with one extra dimension. An important distinction between the radion and the Higgs boson is that the radion would couple directly to gluon pairs, and in particular its decay products would include a significant fraction of gluon jets. The radion has the same quantum numbers as the Standard Model (SM) Higgs boson, and therefore they can mix, with the resulting mass eigenstates having properties different from those of the SM Higgs boson. Existing searches for the Higgs bosons are sensitive to the possible production and decay of radions and Higgs bosons in these models. For the first time, searches for the SM Higgs boson and flavour-independent and decay-mode independent searches for a neutral Higgs boson are used in combination to explore the parameter space of the Randall-Sundrum model. In the dataset recorded by the OPAL experiment at LEP, no evidence for radion or Higgs particle production was observed in any of those searches. The results are used to set limits on the radion and Higgs boson masses.