The Wikipedia entry for Earlswood Lakes, the reservoirs for the Stratford upon Avon Canal states that Prisoner of War from the Napoleonic Wars with the French were used to construct Earlswood Reservoirs as this first happened between 1821 and 1823 it is less likely to have been the case and the reference is given as from the Earlswood Craft Centre. By 1821 it would be reasonable to assume that the prisoners had been repatriated.
Authority to make the reservoirs was made first by the 1815 act, but the act of 1821 also dealt with water supply and it seems that was the act that led to the principal work commencing and the reason for that was the anticipation of additional traffic travelling to Stratford and onto the Stratford & Moreton Railway/Tramway.
There also another bill in 1836 which mentioned improvement of the reservoir.
The engine house was completed in 1823 and the bulk of water from the reservoirs were pumped using the beam engine there.