From the army officer lists covering the period it would appear that up to 1803 the majority of British regiments were single battalion, and with eight companies maintained on the strength with roughly 3 officers per company.
The Guards were an exception being multi battalion and closer to ten companies per battalion. The 1st regiment of foot and a couple of others had two battalions.
From 1803 the battalions started to be made up to ten companies, with a fuller complement of officers, and extra battalions added to each regiment, usually only one extra. At first the extra battalions tended to be the recruiting pool for the first battalion, and so often weaker. You can see quite a bit of this in the Peninsula with second battalions having the cadre sent home to recruit from fresh, while many of the men were drafted into first battalions.
They were not otherwise treated as regiments with the second and first battalions not normally serving together.
Times at which all this was done, the number of battalions, and the logistics due to some battalions being posted far overseas caused the variations.