For tactical and political reasons of their own, both have opened the door in recent weeks to a referendum on the subject. It will be extremely difficult for either to close it again without provoking a backlash from the anti-European lobby or giving theother a tactical electoral advantage.
And given the innate anti-European sentiments of the British electorate, which would probably vote No to Brussels in three years out of four, and the vociferous and unopposed campaign the Eurosceptics are already running, the chances of a favourable votein a referendum look slim.
The question of a single currency remains a theoretical one for the moment.
It will be some years before sufficient countries in the European Union will be able to meet, let alone maintain, the demanding convergence criteria that were set at Maastricht. But the Prime Minister will now be under continuous pressure from the Eurosceptics in the Conservative Party not to agree to a single currency without a referendum.
Given his evident terror at the thought of taking an unpopular decision, Tony Blair is equally unlikely to support a single currency ahead of an election without a referendum. Even if he wins the election, it is no certainty that he could push it throughwithout a damaging split in the party.
The case against a single currency is easy to make simply by drawing on the raw patriotic sentiment for which the pound sterling is a potent symbol. The public voted in favour of British membership of the Common Market by a majority of two to one in 1975. But circumstances then were very different.
President de Gaulle had tried to keep us out, which only made many stubborn Britons keen to join. UK membership had also been actively sold to voters by the Heath government as a way of opening new markets inside the Common Market's tariff wall, which was a more significant barrier to the free movement of goods than it is today. The Wilson government also gave membership its seal of approval.
The question of political union seemed a long way in the future. A common currency was an even more distant prospect. This time round the future of the currency is a central issue, with profound implications, but there has been little sign of rational debate on the subject.
The business community makes no secret of its support for a single European currency as a means of eliminating the costs and uncertainties involved in trading with the Continent. But apart from a brief effort to point out that the high costs of buying and selling foreign currency for Continental holidays would be eliminated, the campaign to persuade the general public of the merits of waving goodbye to the pound has so far failed to get off the ground.
It will, however, be all too easy to mount a populist campaign to save the pound as a currency, which could be difficult to resist, even assuming endorsement of a single currency by the main political parties.
And if the two main parties refuse to give the electorate any guidance, in case they split their own supporters and alienate more voters than they please in the process, the chances of the argument being decided by emotion rather than reason become even stronger.
The real issue is not what the European currency is called, but who controls it. Whether control goes to a European federal government, or an independent European central bank, the implications for policy-making are profound. For one thing, giving up control of the currency permanently blocks the option of devaluation, which is what, we now know, gave the UK economy a new and necessary lease of life in 1992.
Giving up control of the currency does not immediately mean that national governments lose overall control of economic policy. But in effect that is what will progressively take place. A common currency implies common interest rates, for example: otherw i se domestic lenders will move their funds in the direction of the highest rates in other countries, and borrowers towards the lowest.
A government that operates a common currency can still in theory raise and lower its public spending, and raise and lower taxes to suit its own political and social policy requirements. In practice, only the strongest economies - which means perhaps onlyGermany - could act autonomously in this way, as the Germans did while they were financing the integration of the old East Germany.
Other governments that tried to operate inappropriate fiscal policies, such as high taxation, would risk driving capital investment away, unless taxes were balanced (as in Germany) by high levels of skill and productivity, or (as in France) by an industrial structure that resists pure market forces.
The UK no longer has that kind of insulation. Our skill levels and productivity remain below average European levels, and our own public and private sector companies have deliberately laid themselves open to competitive pressures in the push for maximum profit. For better or worse, capital can flow very freely in and out of Britain.
Current UK economic and social policy is based on under-cutting our partners. But a common currency would force economic policies to converge and where economic policies lead, social policies will probably follow. The key issue that Britain should be voting on in any referendum is whether it wants to embrace this kind of common future or not.
The Eurosceptics of course are convinced they can persuade the rest of Europe to join them in rejecting a single currency before it has any chance of being adopted. But it would be wrong for the UK to underrate the strength of the European ideal on the Continent, or to assume the single currency will never happen.
It is possible there will be a two-stage Europe for some years with a core of countries operating a common currency, and an outer rim still striving to attain the common standards required. But it is hard to see how the public could be asked to vote in areferendum for some sort of permanent state of limbo, which preserved the opt-outs negotiated at Maastricht indefinitely while other countries go ahead with a single currency.
A referendum ought to ask a single question inviting the answer Yes or No. If the positive case for voting Yes is the harder one to make, the consequences of a No vote could be severe. Rejecting a common European currency if the core European countries approve it is likely to cause a deepening rift between the UK and those countries. It would leave Britain ideologically pure in its commitment to open competition in a world marketplace, but in danger of isolation and exposed to the growing competition from low-wage, hi-tech economies in Asia.
It is hard therefore to think of a more important issue. There are powerful democratic arguments for allowing a popular verdict on such a far-reaching issue. The danger that Mr Major and Mr Blair are courting is that, in the absence of positive guidance,any decision will now be taken in a referendum based on emotional and parochial reasoning, rather than on the core economic arguments.