I have had this watch for sometime without much in the way of research largely because I couldn't find a QSA roll entry for Atkinson and wasn't entirely sure this was Boer War related.
The engraving to the rear reads
Presented to Surgeon Captain J R Atkinson R.E.R. Vols by Crew L.N.E.R. 1902
I have now found an obituary from the Northwich Guardian, November 19th, 1912 which puts the watch into context
and with this additional info I have found him on the roll of No 1 General Hospital
His name appears on the Crewe memorial six names down in the left hand column
He is mentioned in several places in the excellent book
From Crewe To The Cape by Potts Marks and Curran and on page 137 it is noted that
At Crewe Engineers HQ, the retirement of Surgeon Lieutenant Colonel James Atkinson (Dr Atkinson) was announced. This is presumably the older Dr Atkinson, the father of Surgeon Captain Atkinson. On page 154 it states
that On March 4th (1903),
Surgeon Captain James Reginald Atkinson resigned his commission in the Railway Volunteers.... Many events were held in Crewe to celebrate the return of the volunteers and I am unable to identify the specific occasion of the presentation of the watch.