Simple answer to the original question: the UK goes bankrupt and ceases being a significant international economic or political player about 15 years earlier than actually happened, conceivable oil stockpiles are largely irrelevant.
In the period 1945-1968 (and beyond) the pound was continually experiencing exchange rate crises, there was one about every 2-3 years. There were a couple of reasons for this this. Firstly there was the issue of sterling balances: the British had paid for lots of stuff in pounds during WW2 (a privilege they got from the sterling area), so many countries had large amounts of sterling which would be converted into other currencies if there was any threat of sterling devaluation. These were valued at about £3.5bn in 1945 (about 35% of GDP) and are completely separate from the debt owed to the US (which was in $). Originally this money was owed to countries like India, Egypt and Argentina, largely poor countries which would bitterly resent being defaulted on by a wealthy country. The second factor was that the UK typically ran its economy slightly too hot, with unemployment slightly too low and inflation slightly too high. Whilst possibly good in the short run, this meant that, combined with a fixed exchange rate, UK goods became increasingly overpriced and the British were unable to export enough to run the current account surplus needed to pay off the sterling balances, instead what tended to happen was that some countries got repaid by borrowing from others and the holders of sterling increasingly became Middle Eastern Oil exporters.
So why does this affect the Suez crisis? Currency crises are not linear events, they happen like a bank run, if nobody else wants to convert their money from £ into say $ then you can get your money, but if everyone tries to do it at once then only those at the front of the queue will get their money, giving rise to self fulfilling prophecies. It was exactly such a crisis that suez triggered: trouble in the middle east threatened to raise the global price of oil, the blocking of the Suez canal would raise the price of a large share of British imports and exports (not just oil), military mobilization would reduce UK exports. All of these would threaten the UKs balance of payments so people ran to be at the front of the queue without the US needing to do anything. Just like with a bank run, in a temporary currency crisis the solution is for a lender of last resort to loan you the money to tide you over, this is the IMFs role. An IMF loan would need US approval and it is here that the US was critical. The US didn't need to do anything to force the UK to stop, mere inaction was enough. France didn't have the issue of large quantities of francs being held by foreigners, so France wasn't as vulnerable as the UK to US displeasure.
Once the UK agreed to stop the operation an IMF loan was fairly rapidly agreed. The alternative in 1956 was for Britain to default on its debts to foreigners on a large scale, ending its position as a global economic/political power far more decisively than happened OTL (plus ending its close relationship with the US, possibly forever). Going back before 1956, if the UK had run larger balance of payments surpluses (and stored them either as foreign exchange reserves or possibly in the form of oil) from 1945 it might not have been in the same position, but to make a significant dent in the sterling balances this would have meant (over most of 1945-56 at least) higher unemployment and a lower standard of living, which given rationing continued until 1954 in OTL was fairly unthinkable at the time.
This is assuming that Suez was a good idea in any case, even setting aside the moral dimension. The best plausible scenario is one where a successful operation would merely have returned the British to the pre-1954 position, i.e. fighting an unsustainable static guerilla war in the canal zone. The British (and French) simply underestimated the strength of Egyptian nationalism.
