Longer than France can supply themselves. If I remember correctly Britain's economy actually did pretty well during the war. But as
funnyhat pointed out, the real issue was exhausting political capital rather than exhausting actual money.
Actually, situation was quite complicated:
"Total British debt increased from £229,614,446 in February 1793, to £497,043,488 in February 1802 and to
£816,311,939 in February 1816." (
http://resmilitaris.net/ressources/...itary_mobilization_in_the_napoleonic_wars.pdf). Which was almost
almost 200% of GNP.
Now, the allies:
"in 1813 the British provided £7,000,000 to the Prussians and the Russians in order to fight Napoleon. Another £1,000,000 was given to Sweden in order to form a 30,000-strong force and fight the French on the Continent. In total, for 1813 British military aid to its allies was £11,294,416 and an additional sum of £11,355,412 came from war loans. Thus total British aid for 1813 to its allies was £22,649,828."
Russia did not consider the British financial help adequate and in April 1813, the Russian fiscal situation was so critical that policy-makers fully expected the banking system to collapse completely if war operations were prolonged for another year or more (Russian government spending increased from 79,303,355 roubles in 1802, to 287,541,557 in 1812).
In Prussia accumulated war-related debt covered by the public borrowing in 1810 reached 100 million thaler, 132 in 1813 and at least 218 in 1820.
"Austria’s participation in that Fifth Coalition against Napoleon only occurred after British promises to the Austrian Emperor of financial aid, and of military action in Italy and Holland in order to tie down French troops... Austria’s economic mobilization was also important and, just as in the Russian case, relied heavily on money supply increases. To illustrate, in September 1806 money circulation was just 440,549,000 paper gulden ; in July 1810, it was increased to 1,011,801,000 paper gulden. In February 1811, the exchange rate between a paper and a silver gulden was 12:1. At that point, the Austrian government decided to impose new rates, which accelerated the currency’s depreciation. 77 The war proved financially catastrophic." Only £250,000 in silver bars materialized.
In other words, it was not only an issue of Britain agreeing to pay subsidies but also ability and willingness of the continental countries to contribute the huge amounts of their own money (and people) for a war effort. Not that Britain would be able to keep increasing the national debt forever.
OTOH, "The industrial index of France was stronger than Britain’s. To illustrate, coal production increased from 250,000 tons in 1794 to 800,000 in 1814. The production of iron increased from 60,000 tons to 112,000 tons and salt-mine production increased from 40,000 tons to 150,000 tons over the same period.93 In this time frame, France’s arms industry went through a steep and immense transformation."
"Yet, France’s budget could hardly compare with Britain’s, of which it represented a fraction: 36% in 1805, 42% in 1813. In spite of the exploitation of occupied countries, the French debt increased from 47 million francs in 1809 to 220 million in 1813. By 1814, the fiscal situation had become extremely problematic. On January 25 that year, a Cabinet meeting concluded that monthly State revenues amounted to only 367,000 francs, as opposed to the 10 million which would normally accrue in peacetime. French defence spending could not possibly equal the
combined spending of Britain, Prussia, Austria, and Russia. This undoubtedly was one of Napoleon’s greatest sources of weakness."
So it seems that the key component were willing coalition members.