A summary, for your further research:
re-war
Was a member of a Territorial Force (TF) (part time) artillery unit 8th London (Howitzer) Brigade (sometimes written VIII London (Howitzer) Brigade stationed in Plumstead. He would have attended occasional evening and weekend training drills and an annual two week camp.
1914-1917
On the outbreak of war, the TF were mobilized and the brigade began formation training with the division they supported 47th (2nd London) Division .
http://www.longlongtrail.co.uk/army/order-of-battle-of-divisions/47th-2nd-london-division/He arrived in France with the division on 16 March 1915. His brigade changed its title to 238 Brigade (also written CCXXXVIII Brigade) which comprised two sub-units, 21st and 22nd Batteries. Sgt Horner belonged to 22 Bty.
The war diary for 238 Brigade, which unusually has the odd page written by the batteries, is at
http://discovery.nationalarchives.gov.uk/details/r/C7354535This covers up to January 1917 but should be read up to May 1916 when 22 Bty of 238 Brigade was moved in a re-organisation to become D Bty of 236 Brigade, (written D/236) still within the 47 Div artillery. The 236 Brigade diary is at
http://discovery.nationalarchives.gov.uk/details/r/C7354532, start at May 1916. While we don’t have his record to prove it, it would be normal for all the personnel of the battery to move across to the new battery so it would be sensible to read the 236 Brigade diary from May 1916.
Late 1917. This is where we have to make a leap of faith! It is understood that he spent some time in Italy in 1917. The only British involvement in Italy was a short lived campaign from November 1917 to early 1918. This is covered here
http://www.1914-1918.net/italy.htm. The 47 Div did not take part in this so, although we don’t have any record to support it, we could say he was posted to one of the howitzers brigades that accompanied this force (102, 103 and 72). The diaries for this period are at the National Archives but have not been digitised and as we don’t know which he belonged to, you may wish to think whether it is worth having them copied.
Early 1918 to end of the war. Problem – which unit did he belong to, did he stay with whoever he was with in Italy, did he return to 236 Brigade or did he go to another unit entirely?? Without records – difficult.
MaxD