The difficulty in establishing an average strength for British Battalions, in 1805, is mainly that the establishments for the different regiments were not uniform. I have no explanation as to why this was so.
For instance, a number of two battalion regiments had a total establishment of 1,390 men. Others had an establishment of 2,000 plus men. It does appear that the 1st Battalions had a higher establishment than the 2nd Battalions had. Those on foreign service averaged 900 men for 1st Battalions and only an average of 600 men for the 2nd Battalion at home.
The Garrison Battalions had an establishment of 513 men while the Royal Veteran Battalions had an establishment of 740 men with two having 953 men.
The Life Guards averaged 410 men, The Royal Horse Guards had 645 men. The 1st Dragoon Guards had 1,083 men while the remainder had 905 men. Eight Dragoon Regiments had 1,125 men and eleven had 905 men while the 25th Lt Dragoons had only 727 men.
The 1st Foot Guards had an establishment of 4,267 men while the Coldstream Guards and 3rd Foot Guards had 2,667 men each.
I could not find an establishment set for the Foreign Troops, many were just forming, but the West India Regiments had an establishment of 1,124 men.
Hope this helps somewhat.