Likely the London & Scottish Volunteer Rifles raised in 1859 by the famous Lord Elcho as their Lt. Colonel. Elcho was the paramount target shooter of his time and a major influence on the rise of precision long range target shooting in the UK. As well as the prime mover for the Volunteer movement itself. His men, and certainly his officers would have been crackshots and had the very best equipment. A man of great skill, determination and influence. The Elcho Shield is a competition started in 1860 with eight man teams from England, Scotland, Ireland and Wales. Still shot today at Bisley at 1,000, 1,100 and 1,200 yards. Won by England in 2013.
This rifle is, without doubt, an important historical artifact. I can't advise myself but I would want to take good advice if it were mine before such a restoration to ensure I wasn't devaluing the piece both financially and historically.
There is a London and Scottish Regiment Museum. They might be able to help regarding the names on the shield. Or perhaps the (British) National Rifle Association based at Bisley.
Good luck. One lucky owner.