If you look to the thread header, you'll see that the main point is "How long can Britain supply France's enemy?". Because - and let's face facts here - whether the credit rests with British subsidies and diplomacy or Napoleonic avarice and hubris, Britain never spent particularly long without a "France's enemy" to supply. You cite Tilsit, but in the immediate aftermath of Tilsit Britain was gifted Spain and Portugal as allies by imperial overreach; within two years they've built the Fifth Coalition with Austria, and within six years they had both Russia and Prussia fighting against Napoleon. Absent a massive and completely ahistorical change of attitude from Napoleon himself, it's highly unlikely that European powers will be happy to live with France in the way you suggest, and discussing it here adds little to the question posed by OP. Indeed, it verges on derailing the thread, and I'm sure you'll understand my declining to engage in it further.This depends on what the main point is.
It seems what's been really missing from the thread is a decent explanation of why British financial capacity is so much greater than that of France. In the hope that it contextualises some of the broader issues, let me attempt to provide one. Britain, in comparison to France, has a long history of creditworthiness. The ancien regime was infamous for defaulting on its debts, and the Directory did the same in 1797: conversely, most people who have lent money to Britain in the past have got it back, and are therefore willing to do so again. Britain's cost of borrowing never rises above two-thirds of that of France even at the very worst times. Furthermore, creditworthiness enables Britain to use a much wider variety of fiscal tricks beyond the pure raising of loans, from issuing paper money and paying with government drafts to suspending convertibility in specie - none of which are open to the French.Though I do feel that while its established that industrially and logistically the British could maintain a near indefinite supply, I don't think that we have covered whether they could have continued the effort monetarily. Did they really have the money to spare to keep paying large subsidies forever? It was mentioned that the Coalition budget was far larger than the french, and that the french suffered from a loss of revenue because of the war. Did the Coalition not experience the same difficulties, or just to a much smaller degree? and does Britain have the capacity to continue this huge war budget for say, another 5 years?
Moreover, the British political system is far more transparent and responsive to public opinion than France. British governments have to have their budgets approved by Parliament; Napoleon's budgets are secret. This doesn't just mean that the British government is in constant communication with the holders of debt, or the c.120 MPs representing financial interests who sit in Parliament. It also means that there is a greater degree of buy-in for the everyday taxes on commodities like alcohol, which support the much higher proportion of borrowing. This is, of course, helped by the greater sense of shared national identity felt in Britain in comparison to rapidly-expanding Napoleonic France.
Control of the sea gives Britain other considerable advantages. It can bring in gold and silver from the South American colonies, which reduces the inflationary impact of printing money. By contrast, France is reduced to paying a heavy commission to smugglers to bring bullion from Britain. Britain can import goods from its colonies and trade with neutral powers, bringing in money from customs duties to support borrowing. Due to both British control of the sea and the short-sighted imposition of the Continental System, French customs revenues drop from 51m francs in 1806 to 11.5m in 1809. Furthermore, we see capital flight from Europe, with wealthy families such as the Rothschilds decamping to Britain. Both these processes force France into even greater reliance on internal revenue, which compounds their existing domestic political difficulties.
The main way in which France attempts to mitigate this is by forcing the cost of war onto others, through hefty indemnities imposed on defeated enemies, plundering occupied territories, and requiring allies to pay contributions or supply soldiers to France. Of course, these methods build resentment within occupied Europe, and help to explain why Britain found it so easy to build coalitions by simply offering to subsidise a portion of the costs of war. But I digress.
The real question is: how long could Britain keep this up? Although it's kind of like predicting when an elastic band will snap, there doesn't seem any intrinsic reason why Britain can't keep it up as long as she needs to - certainly long enough to outlast France. France has already tried and failed to cut off British colonial support; she can't really do anything to shake faith in British creditworthiness, or undermine faith in the political system. As people have noted, if she continues to win victories, it might reduce domestic support for the war. However, France was trying to do this in the first place, and victories are almost certainly more costly in money, men and materiel to France than they are to Britain - particularly in Spain, given the nature of guerrilla warfare. In reality, therefore, attempting to defeat Britain in this way may simply bankrupt France before it drives Britain to the negotiating table. Alternatively, she could eke out her existing finances by pushing more of the costs onto the rest of Europe - thereby helping to build coalitions on Britain's behalf.