If a second Britain from 1812 entered the Second World War

How would the Second World War change if an island containing Great Britain as it existed in 1812 appeared west of Ireland?

After an authority crisis, its greatest value would be retrainable manpower, food, timber, and protected production space rather than its wooden warships.

The first problem would be political authority because an 1812 government would not automatically recognise Winston Churchill's Britain. If the two states cooperated, Napoleonic-era soldiers could be retrained with modern rifles and used to replenish wartime manpower under experienced modern non-commissioned officers. Higher twentieth-century wages, better weapons, and medical care would make service attractive despite the enormous training burden. The duplicate island would also provide food security and territory beyond the easiest reach of German bombing. Its timber and skilled carpenters could support large-scale Mosquito construction, illustrating how raw materials and labour can matter more than the obsolete fleet that arrived with them.