You may be surprised at what interest there would be in the rifle even in it's present condition.

The magazine first off should have the cartridge guide indentations on the side walls extending completely to the bottom of the sides.
Magazines for the later #4 rifle have the guide indentations stop about 1/2 inch from the bottom. I think the pic shows a proper magazine for a MkIII rifle.

The back edge of the magazine (spine) should have a number stamped into the lower portion.
Most likely a '4'. That is a standard WW1 type magazine assembly for the Mk7 ammo. Also proper would be one marked with a '3'.
Those are older #1 & #2 magazine assemblys that were made for Mk6 ammo, but converted for use with the later Mk7 ammo.

These #3 magazines also have a rivited pivoting 'stop clip' on the upper right hand side wall of the body to ID them. The #4 does not.

Both #3 and #4 magazines have a small spring clip rivited to the lower spine of the case (takes care of magazine 'rattle'!) and that number is stamped just below it. Collectors like the #3 magazines and pay a bit more for them.

There should NOT be any serial number on the magazine at all. The only SMLE mfg to serial number the magazines was Ishapor (India).
So there is no telling if the magazine is THE magazine the rifle left the factory with. But if the small inspectors mark, also on the spine, is that of the LSA factory, it then matches the mfg and is another plus for collectors/restoration.

The LSA inspectors mark would a Crown/X/number.
'X' was the letter used to denote LSA mfg.

These rifles are rightly called MkIII or MkIII* 'SMLE' or 'ShtLE'
The use of the No1 designation did not come till 1926 when a change in nomenclature was approved.

Up untill that time the SMLE was designated only by a 'Mk'. The '*' given to show changes with in the Mk designation.
In 1926, the SMLE became the No1 (in both MkIII and MkIII* variations),,the .22calRF training rifle became the No2, and the Pattern '14 303 rifle became the No3.