The death of a soldier was registered in the same way as a civilian (even if he lost his life overseas) and a copy death certificate can be ordered from the General Register Office (England and Wales office).
How to find these records
For deaths that took place within Great Britain:
If a serviceman or woman died within Great Britain, the registration of their death will have taken place in the district in which they died.
Example: Horace Henry Moorhouse, a soldier of the Royal Engineers, died on 23 October 1917 at the 2nd Southern General Hospital in Bristol. He is buried in Manchester Southern Cemetery, not far from his home in the Longsight area of the city. Horace was aged 20.
His death was registered in Bristol and appears in the normal index of registered deaths. These indexes can be obtained online at Ancestry, Findmypast, TheGenealogist and other sites. A copy of his death certificate can be obtained from the General Register Office, using the details given (name, year, quarter, volume and page number).
For deaths that took place overseas:
If they died overseas at or sea, the death was not registered in a district at home but can be located in a centralised General Register Office index.
Example: Albert Townsend, Pte 19964 of the Wiltshire Regiment, was killed during the Battle of the Somme in 1916. He has no known grave and is commemorated at the Thiepval Memorial.
He is listed in the “Index to War Deaths 1941-1921 Army (Other Ranks)”. A copy of his death certificate can be obtained from the General Register Office, using the details given (name, rank, number, regiment, year, volume and page number).
There are similar but separate indexes for army officers and for men of the navy.
The indexes can be found at Findmypast and TheGenealogist.
What would appear on the death certificate?
Beware: there is a price for obtaining a copy and it may not add value to your research.
The death certificate may not give much information beyond that found in the Commonwealth War Graves Commission “Debt of Honour” register and “Soldiers Died in the Great War”. It is unlikely to give an accurate cause or place of death and is most cases will merely state that the man was killed in action, died of wounds or even just “died”.
Registration of the death within the theatre of war
I hope to add a section on this complex matter in due course.