Nope, not quite.
Safety on the left is a Lee-Enfield, either a Number 4 or the earlier SMLE, which ran through several Marks.
Safety on the right means a Pattern '14 rifle, later called the Number 3. It is a Mauser redesign wich saw service in both Wars, often as sniping equipments.
Your rifle obviously is a Lee-Enfield and is marked as "III", so it is a Short Magazine Lee-Enfield Rifle Mark III (if built before 1927) OR a Number 1 Mark III (if built after 1927). They are exactly the SAME rifle, just the name was changed. Does yours have a * after the III? What is the date of manufacture? Should be there, just above that III.
You need a safety for an SMLE...... which is also called a Number 1 Mark III.
As above, Woodchopper has mentioned that he has spares so you an get that piece of history safe again.
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