Here are images from the 1912 Westley Richards catalog that show a folding peep sight identical in appearance to those used on the Mannlicher Schönauer:

"...a peep sight, as illustrated, sunk into the grip can be fitted if desired."

The full page:

They also offered their Mauser based sporter as a 'Lightweight .318 Magazine Rifle', available with the 'flip up peep sight', which used a takedown system very similar to that of the pre WW2 MS:

" Flip up Peep Sight on grip, as illustrated on page 103, at an extra charge of £2 2 0."