Over fields of characteristic zero, there are well known constructions of the irreducible representations, due to A. Young, and of irreducible modules, called Specht modules, due to W. Specht, for the symmetric groups Sn which are based on elegant combinatorial concepts connected with Young tableaux etc. (see, e.g. ). James  extended these ideas to construct irreducible representations and modules over an arbitrary field. Al-Aamily, Morris and Peel  showed how this construction could be extended to cover the Weyl groups of type Bn. In  Morris described a possible extension of James' work for Weyl groups in general. Later, the present author and Morris  gave an alternative generalisation of James' work which is an extended improvement and extension of the original approach suggested by Morris. We now give a possible extension of James' work for finite reflection groups in general.