Most obvious guess for RM would be "Royal Marines", as in the Royal Naval Division of WWI fame. The fact that rifle still has that disc would suggest it "left the service" by other than the usual methods. Take off the handguard and look for two digit dates on the barrel near the receiver/body.
The Zeebrugge raid comes to mind as one way a rifle might have suddenly "left the service" and survived in such a state so long, but there are many others, in both world wars.
11 35 does look strongly like a date, but that's beyond my knowledge of marking discs.