It looks a lot like one of the many BSA Sporters made on the P14 after WW1. Sporterized Military stock, cut down rear rcv'r to elliminate the 'ears', quite a few different rear bbl sights were used including this simple open sight on the one in the link and a 2 folding and one standing leaf rear sight. Some checkered stocks some not, Some just the pistol grip.
MAde into different calibers too. There's an old BSA ad for the sporter in 8x57Mauser round,,'commonly available around the world'.

BSA usually marked them either on the bbl or on the action itself 'Manufactured by BSA'.
Could be covered by a 'scope mt base on the OP rifle.

They made a Model E Sporter later on with a commercially made sporter stock. ParkerHale retailed those I believe. Same P14 actions and bbl's actions w/ some modifications and alterations.

The WR marking could be a retailers marking w/caliber,,not unusual on another mfg's firearm.
There's another engraved line above the WR marking in the photo facing the op direction. Can't read it though. Looks like larger and more stylized lettering than the WR marking. One portion might read 'Co Ltd' (?).

Just one I found a pic of. There are plenty BSA P14 Sporterpics around,,
http://www.icollector.com/BSA-P14-SPORTER-RIFLE_i24241426

Just my observations..