We don't know who J Baker was, nor anything about his relationship to William. It's a bit tricky to work too much out about him from this address, but I take it to mean XI Corps Signal Cables Section. Signallers (Communications people) were needed at all levels in the army, and some would have been assigned directly to the Corps and served there. The fifth division - which William Whitmore belonged to - served with this Corps during the Battle of Hazebrouck during April 1918, and in the action at La Becque on 28th June 1918.

The table below lists all the engagements of the XI Corps. Please note: as with all tables like this one, remember that it lists only engagements with the enemy. Troops would spend considerable amounts of time each year in the trenches, and within firing range of the enemy. Shelling and sniping would be a permanent danger, which lessened (but did not disappear) when there was no major engagement.

Campaign Battle Dates Present
Battle of Loos Battle of Loos 25 Sept. – 8 Oct. 1915
Action of Hohenzollern Redoubt 13 Oct. - 9 Oct. 1915
Battle of the Somme Attack at Fromelles 19 July 1916
  Posted to Italy Late 1917 - Early 1918
German Offensive in Flanders Battle of Estaires 9-11 Apr 1918
Battle of Hazebrouck 12-15 Apr 1918
Battle of Bethune 18 Apr 1918
  Advance in Flanders 18 Aug. - 6 Sept. 1918
  Final advance in Artois 2 Oct. - 11 Nov. 1918

Taken from The British Army in the Great War, and The Regimental Warpath.