In December 1804, William Pitt signed an alliance with Sweden, Andrew Roberts explains (in Napoleon: A Life), and once Britain had also signed the Treaty of St Petersburg with Russia in April 1805 the core of the Third Coalition was in place:
Britain was to pay Russia £1.25 million in golden guineas for every 100,000 men she fielded against France. Austria and Portugal joined the coalition later.
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Pitt had set the precedent for subsidizing France’s enemies as early as 1793 when he had started hiring troops from the German princes to fight in the Low Countries, but he was often deeply disappointed with his investments, as when the Prussians seemed happier to fight the Poles than the French in 1795, or Austria took the Veneto at Campo Formio in 1797 in return for Belgium (and peace). Overall, however, the subsidy policy was seen by successive British governments as well worth the cost. Napoleon naturally characterized it as Britain being willing to fight to the last drop of her allies’ blood. ‘Please have caricatures drawn,’ Napoleon ordered Fouché in May 1805, of ‘an Englishman, purse in hand, asking different Powers to take his money, etc.’
In 1794, payments to allies amounted to 14 per cent of British government revenue; twenty years later, with Wellington’s army actually inside France, it was still 14 per cent, although the British economy had grown so considerably in the intervening period that this now represented £10 million, a vast sum.
That 12.5 pounds the British paid for each Russian soldier was significantly more than the seven pounds and six shillings the British paid annually to the Grand Duke of Hesse for each of his soldiers during the American War of Independence.
Keynes said the British were bankrupt by 1915. If they’d found mercenaries to feed German artillery they’d have been better off even if they’d paid high dollars (thanks John) for the meat.