Just for historical accuracy the dates of formation of British Engineer units are not correct. I have recently researched the detail from the original records in the National Archives. The Royal Military Artificers were formed in 1787 on a 6 company establishment. This was expanded to 12 companies in 1806 and 32 companies in 1811. The unit was re-titled as Royal Sappers and Miners on 23 April 1812 but there was no change to their establishment, just the title and adoption of red uniforms rather than blue. The 1811 establishment for each company was 1 sub-lt, 5 sgt, 5 cpl, 5 2nd cpl, 15 carpenter, 10 mason, 6 bricklayer, 4 smith, 2 wheeeler, 30 miners, 1 cooper, 2 collarmaker and 3 drummer.
The massive expansion in 1811 was clearly prompted by Wellington's frustrations in the Peninsula but it obviously took time to train these men and then post some additional companies to the campaign area.