AP#14 BR 1st Army, 1 Corps
The BEF was divided into the First and Second Armies on the 26th of December 1914 and thereafter no longer existed as a nominal unit. These armies were thus not separate reinforcing armies but the new denomination of the forces that incorporated the BEF.
I consider the first British reinforcing army to be the expansion of the BEF due to the addition of divisions constituted by volunteers from Territorial Army units. Then, when the second reinforcing British army is brought into the play, the BEF is removed and may be substituted by that army, representing the consolidation and change of denomination, and leaving First and Second Armies in place of the BEF, as historically. If all BEF units have been removed from the map, the army will represent new levies assembled in England.