But Sir Mervyn warned that any recovery would be slow and that the crisis in the eurozone had cast a "black cloud of uncertainty" over businesses around the world.
In his first live television interview, Sir Mervyn told eurozone finance ministers that "now is the time" for them to settle the future of the currency.
In a wide-ranging interview on Channel 4 News, Sir Mervyn cautioned Chancellor George Osborne not to water down the proposals for reform of the UK's banks proposed in Sir John Vickers' review.
And following reports the Government could miss its target of beginning to see national debt falling by 2015/16, Sir Mervyn said that would be acceptable only if the global economy was growing slowly.
Sir Mervyn said he had predicted a "zig-zag year" for the UK economy.
"The last quarter was down, I think the next quarter will probably be up," he said.
"I think we are beginning to see a few signs now of a slow recovery, but it will be a slow recovery, after a banking crisis one can't expect to get back to normal and I fear it will take a long time."
The recovery would depend on events in the euro area and in other economies such as the USA and China.
The eurozone countries had been working hard to avoid triggering a Lehman-style collapse in the markets, but there was no "guarantee that they will be able to do that".
Sir Mervyn added: "I think it's this black cloud of uncertainty which is hanging over British business as it is hanging over American business."
The European Central Bank's actions to support the currency had bought some breathing space, Sir Mervyn said.
"Now is the time that they have to decide exactly what kind of monetary union they want," he said.
Sir Mervyn acknowledged that a break-up of the eurozone would be "extremely difficult for all concerned" but "we would come through it" and preparations had been made for such an eventuality.
"I think it would have been irresponsible not to have made preparations or contingency plans for it," he said.
Sir Mervyn said the actions necessary to reform the UK's banking system were "straightforward" but would depend on Parliament.
The Vickers report recommended a ratio of 4% equity to gross loans and investments but the Government's white paper supports a 3% ratio following lobbying by the banks.
Sir Mervyn said: "I think the original Vickers proposals were very sensible, I personally would support them.
"But what's more important than anything else is that we actually implement them.
"The Government has said that it will give the Bank of England the power to impose a leverage ratio, a limit on the amount the banks can borrow, in 2018 and I think it's important that they do that."
The other key recommendation by Vickers was to ringfence banks' retail and investment operations.
Asked whether he would have preferred total separation, Sir Mervyn said his "instinct" would have been to go "more in that direction".
But the Vickers proposals on ring-fencing had not been "significantly" watered down, the Governor said.
Sir Mervyn has previously endorsed the coalition Government's "textbook" response to the economic crisis.
He told Channel 4: "The plan did allow for the fact that if the economy were to grow slowly then taxes would not rise as quickly and spending would be higher so the deficit would be bigger.
"The plan said don't attempt to bring that deficit down if it's the result of slow growth in the economy, and that's exactly what's happened."
Sir Mervyn effectively gave his backing to Mr Osborne announcing that the Government will miss its debt target, as long as it was the result of an international downturn.
"If it's because the economy has grown slowly, yes indeed and that was always part of the plan," he said.
"If it's because the world economy has grown slowly, so we in turn have grown slowly then it would be acceptable to be in that position.
"But if the world economy were to pick up and we could grow quite quickly then it would be not acceptable to miss it if we had no real excuse for it."
Sir Mervyn defended the use of quantitative easing as a short-term measure, claiming it had averted a "deeper recession".
"But in the long run we know that we need to spend less and save more," he said.
"And we know that Germany and China need to spend more and save less."