Hi,i was doing research on this and other rifles to actually bid on this rifle and actually found some posts and images on reddit about this exact rifle. In the links/pictures you can see its the exact rifle from the serial number on the bolt and on the left side of the rifle the stock repair above the magazine is visible and the same. Anyway here are the links to post on reddit and also the photos of the rifle on Imgur which shows better close ups of the scope base and rings like you wanted. Was curious aswell what you guys thought:
Looks like Santa delivered early-- A 1915 Lee Enfield No.1 Mk. III Sniper with Periscopic Prism Company Scope : guns
Lee Enfield No.1 Mk. III Sniper with Periscopic Prism Company Scope. - Album on Imgur