Seat post sizes not necessarily straightforward.
I have two 708 frames, one will just about take a 27.0 but has had a hard life so may not be what it was originally. My other 708 was built by Peugeot’s Prestige workshop, an unridden team bike, and is a very smooth fitting 27.2. Reynolds advised: ‘it is common to find internal distortion during the brazing process at the seat lug of the frame. In such instances it is recommended that the seat tube is reamed or breached before attempting to fit the seat pillar’ (from their 1985 catalogue).
I think there were two 708 tubesets, the classic and one for touring, which might be what you have. I have no info on the touring tubeset, if there is one, but here are the specs for 708 classic:
This doesn’t give seat post size for 708, unlike 753 and 653, but my maths says 28.6 – (2 x .6) = 27.4 - .4 = 27.0. I can’t explain the extra 0.4 mm but this seems to be standard. However, my metric framed 753 and 653 bikes all take 26.8 seat posts, not 26.6 as recommended by Reynolds which has led me to conclude the seat post size is what it is, and not necessarily what it is supposed to be.
Good luck