This thesis discusses evidentiality and presents case studies of selected English verbal constructions that have evidential functions. The constructions have clear evidential functions, but each is problematic in terms of its diachronic development. Two have been the subject of some discussion in previous work: BE going to (e.g. Berglund and Williams 2007, Langacker 1998, Leech 1971, 2004, Nicolle 1997, 1998) and BE supposed to (e.g. Berkenfield 2006,Moore 2007, Noel and van der Auwera 2009, Traugott 1989, Visconti 2004, Zeigler 2003). The other, BE meant to, is in present day English a polysemous construction with a range of uses very similar to that of BE supposed to. The constructions are problematic in different ways and this thesis attempts to resolve those difficulties, applying the notion of analogy in each case. The thesis is framed in a Cognitive Linguistic and usage-based perspective (e.g. Bybee 1985, Croft 2000, Langacker 1987,2008). The thesis addresses three central questions. Firstly, it asks to what extent English can be said to have conventionalised evidential constructions, and how these compare to typical, i.e. morphological, evidential constructions in languages that have an evidential morphology (see Aikhenvald 2004, Aikhenvald and Dixon 2003, Chafe and Nichols 1986). Secondly, it asks to what extent grammaticalisation and other widely cited historical processes, particularly analogy, apply to the constructions in the case studies (cf. Bybee and Pagliuca 1987, Traugott 1989, 2002, Traugott and Dasher 2001). Thirdly, the thesis considers the constraining or "guiding" role of conceptual space (e.g. Anderson 1986, Croft 2000, 2001, Haspelmath 2003) in the development of the constructions. While also referring to descriptive grammars, such as Visser (1973) and Quirk et al (1985), the thesis provides a corpus-based account of the historical development of each of these constructions. I use data from a range of existing corpora such as the Early English Books Online collection, and a corpus collated from freely available 18th century texts. The Helsinki Corpus and the British National Corpus are used for exemplifying some issues. The frequencies over time periods are subjected to statistical significance tests, where appropriate. I show how a usage-based diachronic construction grammar approach can help account for the complexities of these individual constructions. The usage-based theoretical perspective, especially with respect to the process of analogy, is shown to be able to explain some problematic issues that arise with respect to unidirectionality and subjectification in grammaticalisation, and the studies are applied to the Semantic Map Connectivity Hypothesis (Croft 2001, Haspelmath 2003). There are significant areas identified for further research, particularly in the way in which modal domains intersect, overlap and interact.