Upper limits on the cross-section of the pair-production process e+e- -> hA, assuming 100% decays into hadrons, are derived from a new search for the hA -> hadrons topology, independent of the hadronic flavour of the decay products. Searches for the neutral Higgs bosons h and A, are used to obtain constraints on the Type II Two Higgs Doublet Model (2HDM(II)) with no CP violation in the Higgs sector and no additional non Standard Model particles besides the five Higgs bosons. The analysis combines LEP1 and LEP2 data collected with the OPAL detector up to the highest available centre-of-mass energies. The searches are sensitive to the h, A -> qq, gg, tautau and h -> AA decay modes of the Higgs bosons. The 2HDM(II) parameter space is explored in a detailed scan. Large regions of the 2HDM(II) parameter space are excluded at the 95% CL in the (mh, mA), (mh, tan(beta)) and (mA, tan(beta)) planes, using both direct neutral Higgs boson searches and indirect limits derived from Standard Model high precision measurements. The region 1 < mh < 55 GeV and 3 < mA < 63 GeV is excluded at 95% CL independent of the choice of the 2HDM(II) parameters.