No, it's definitely not an M Type. I have one of them and apart from the "anvil" type base, there are too many differences. And even the "anvil" base in the above pics has Myford-style "feet' sticking out where it bolts to the bench. M-types and other earlier Drummonds had complete through-holes in the base for the bolts.
The pictured lathe does look very similar to a pre-war Myford, something like an ML3. But looks like gramps may have made a few mods. Looks more like an ML7-style cross-slide, top slide and apron.
The carriage itself though does not look ML7, due to the odd bits of cast iron sticking out in front of the cross slide that cover the ways, partially. Kind of looks like that part came off a lathe with the ways set further apart. That looks more like Southbend practice — but they were all (mostly?) V-beds, not flat beds, and those carriage extrensions over the ways were longer and thinner looking.
Headstock is a bit of a mystery. Very early Myfordish too.. I would hazard a guess that whatever it is, it was originally pre-war flat belt drive that has been converted to v-belts with that extra spacer on the spindle taking up the extra width the flat pulleys would have taken.
If Tony at the lathes.co.uk site does not know what it is, probably nobody will, but it might be worth a post on the Yahoo groups Myford Lathes group.
Let us know if you find out anything. As a regular user of of my pre-war M-type lathe, I am intgrigued to know what you have there.