Seatpost size (diameter) is a good indicator. The external diameter of steel seat tubes is *always 28.6mm. Expensive tubing has a higher strength to weight ratio and is therefore lighter because it can be used in a thinner wall section. 27.2mm is the standard size for 531 (manganese-molybdinum alloy), 27mm for 501 (Reynolds chromium-molybdinum alloy), 26.8mm (Tange chromoly) and so on.
Re Seatpost sizes-
A bicycle made from 'imperial' size tubing, such as Dawes, would, as you state, have a seat tube with an outside diameter of 1.125" or 28.60mm.
In regard to seatposts-
the 531C (Competition) tube set had a butted seat tube of thickness 21-24SWG (0.91-0.56mm) - this equated to a mean internal diameter of 27.48 and thus utilised a seat pillar of 27.2mm diameter.
the 531ST (Special Tourist) tube set, as used in the Galaxy, had a butted seat tube of thickness 19-22SWG (1.02-0.71mm) - this equated to a mean internal diameter of 27.18 and thus utilised a seat pillar of 27.0mm diameter
Hope this helps
reqards
Stew