Probably made by the Faircut Company in Sheffield, this little lathe seems to have been named after a small town to the north of that city. Two versions were offered: a small plain-turning model (not unlike the much better known Super Adept) and a much larger backgeared and screwcutting type, appearing to have been based on the rather fine Faircut Junior, that was marked on its bed as the "Wakefield M28", However, in Sheffield it was Portass rather than Faircut who were kept busy supplying machines for other retailers to re-badge as their own and examples of the former have been found marked: Altona, A.T.M., B.I.L., Bond's Maximus, "Eclipse" (for the Sheffield hand-tool makers James Neil & Sons) Excell, G.A. (George Adams), Gamages , Graves, James Grose Ltd. of London (the latter chiselling off the Portass name and substituting their own badge), Juniper, Randa, Temmah, Woolner and Zyto, All appear to have been based on established Portass models, nearly always the venerable "S Type", although in every case some small differences, usually down to cost-cutting, can be found. 
It is also though that some Grayson and Ideal lathes may also have been sold using the Wakefield name - and it is entirely possibly (though an example has never been seen) that some versions of the Zyto might also have been re-badged.
If any reader has a Wakefield lathe, or any advertising literature about the machine, the writer would be interested to hear from you.