A European Union mini-summit, to be attended by all heads of state and government, is scheduled for 23 May, ostensibly to speed progress towards a deal on a new European Union treaty, to be signed in June in Amsterdam.
Those present, however, will be interested in more than simply probing Mr Blair on treaty compromises. They will use the occasion to congratulate him on seeing off the Euro-bashing Conservatives, while taking the chance to assess his own European credentials.
As always, it will be Helmut Kohl, the German Chancellor, who will set the agenda of the meeting. Fresh back from his annual Easter slimming holiday in Austria, and fired up by his decision to stand for a fifth term, Mr Kohl will be eager to see whether a New Labour government shows any real desire to lend a hand in building greater European union. Jacques Chirac, the French president, will no doubt proffer some rambling thoughts on the future. Others meanwhile, may sit more quietly, assessing Mr Blair's own qualities as potential leader on the European stage - as an alternative leader, perhaps, to Chancellor Kohl.
The word in many capitals is that Mr Kohl, under pressure at home, is also faltering in his role as chief European visionary. There is said to be a "leadership vacuum" in the union. Flip-flop tendencies from Mr Chirac have weakened French input into the Franco-German engine, which is stalling. "It is an opportune moment for a new kind of leadership to step on to the European stage," said one senior Scandinavian diplomat. "Blair could be the counter-weight to Helmut Kohl. We need a strong alternative voice. And we certainly don't have one at the moment."
Tony Blair has already made clear that he wants to "set the agenda" and "to lead" in Europe. To present himself as a counter-weight to Kohl would certainly be a clever piece of UK electioneering - better a counter-weight than a poodle. But if Mr Blair is to play such a role he must first show he can exercise positive influence within the union, which no British Prime Minister has ever been able to do.
The idea that a British prime minister could become a counter-weight to Helmut Kohl sounds fanciful to many European old-timers.
Britain's Continental partners have seen false dawns over the English Channel before. As long ago as 1960 there was talk that if Britain were finally to join the community it could eventually take a leading role. But how, ask the Continentals, can Britain hope to lead in Europe when its interest has always been to divide the continent? Tommaso Padoa Schioppa, the distinguished Italian economist and architect of EMU, sums up the problem more sympathetically than some. "The UK's old historical reflex of insecurity is embedded deep in British chromosomes and is triggered whenever the Continent tends to unite. It goes back to Philip II or to Napoleon. Maintaining the division of the Continent has been one of the main sources of the UK's strength."
The doubters also point out that even if Mr Blair is himself a convinced European, he would be restrained by British public opinion, whipped into new frenzies of scepticism during Conservative rule. A large dollop of this scepticism is also to be found in the Labour Party, traditionally scornful of the capitalist club of Europe.
The very suggestion that Tony Blair views himself as a counter-weight to Kohl is taken as evidence in some quarters that he fails to understand how the European engine operates. The Franco-German motor has always been, and, in many eyes, always will be, the prime driving force. The motor was first ignited by the tough, pragmatic acceptance in Bonn and Paris that only by joining in intimate partnership of mutual dependency, would the two countries be able to avoid further war.
To alter the direction of this engine, which is set on a fixed course of ever deeper integration, would clearly demand a lot of alternative horsepower and some very convincing alternative goals. Blair has yet to prove he is possessed of either. Pierre Muscovici, a leading French socialist, says: "For a Briton to lead on the European stage he would have to be more unambiguously pro-European than anyone else." Furthermore, many believe that if Britain does not join the single currency, it will not only lose more influence, but could be side-lined from Europe entirely.
The fact is, however, that just like the British electorate, Europeans don't really know what the election of Tony Blair could bring in the long term. Both Tony Blair and Robin Cook, shadow Foreign Secretary, have said enough to suggest that fundamental attitudes to Europe could start to change. There is a clear rejection of the little Englander, offshore-island vision of the future. Mr Blair's willingness to give some ground on the veto suggests that he may not always insist on the paramount sovereignty of Westminster as stubbornly as the Conservatives. In opposition, Labour leaders have been busy networking among socialist leaders on the Continent, building allies in a way the Conservatives have never done.
Ordinary Europeans are looking for new answers, as shades of Euro-scepticism spread across the Continent. There was a time when most Continental Europeans were happy to place faith in the political elite who forged ahead with integration in the name of peace and economic prosperity. But (rightly or wrongly) peace has come to seem a dated objective for Europe. And economic prosperity is hard to boast of in countries such as Germany, where 4.7 million are unemployed.
Increasingly, European people are demanding that the decisions of distant technocrats are explained and justified. They want to know what the European engine's "end station" is.
Helmut Kohl, meanwhile, can only provide the same old answer: more and deeper union. What new ideas are proffered by the old guard - such as "flexible" multi-speed decision-making - are often just a sign that Europe is losing unity of purpose. Jacques Chirac has offered none of the impetus provided by Francois Mitterrand before him. At the Commission a plodding Jacques Santer sits in the seat once occupied by Jacques Delors. Chaotic Italy cannot step into the breach. Spain is not a big hitter. Smaller member states are becoming restless, and, with the prospect of imminent enlargement to the east, they are looking around for new ways of countering German hegemony. "Nobody stands up to Kohl. Everybody just waits on the Chancellor's word," was how one Brussels diplomat described the balance of power in Europe today.
If Blair is to develop a girth to counter that of Chancellor Kohl, it certainly cannot happen by the time of the Amsterdam summit in June, which is likely to be a botched affair. Early on, however, he can set a positive tone by avoiding easy traps, such as overblown trans-Atlanticism, which, ever since De Gaulle, has always infuriated the Europeans. He should watch his language - no Major-style "game set and match" comments after Amsterdam. In fact, Mr Blair might consider giving every cabinet member free French lessons (a language he already speaks proficiently) and a course in consensual politics. Silly hats on trips to Brussels should be banned.
Mr Blair should, of course, fight for British interests - all other countries fight for theirs. He could pay a visit to the Bavarian office in Brussels to see how one of the powerful German Lander fights tooth and nail for its rights.
By the launch of the British presidency in January 1998 Mr Blair should be starting to shape his vision. Criticism there must be. It is part of the culture of complacency in Brussels that to criticise Europe is to be labelled "Euro-sceptic." But Blair must chose his targets carefully, unlike the Conservatives whose attacks last year on the European Court of Justice - the most mature of all the institutions - backfired on them. Let him prowl, instead, around the bowls of the Council of Ministers in Brussels, where he will see faceless officials from national capitals carving up untransparent and often unnecessary deals.
He should not just bemoan the "democratic deficit" but attack it for what it is - Europe's greatest failure of all. He should puncture the endless theological discussions about European defence, and direct Europe's foreign policy to areas of the world where the union has real historical responsibility and political influence- the Middle East being today's glaring example.
And criticism should always be presented in the context of positive, long-term goals. The great failure of today's European leadership is the failure to set out goals which match the needs of the times. The problems facing Europe are monumental: unemployment, social equality, discrimination, democracy, to name but some. Although, since Maastricht, the goal of a fully federal Europe has largely been discarded, British ideas of tailoring Europe down to a simple free-trade area are evidently unrealistic.
Given his own commitment to constitutional reform in Britain, Blair might take a lead in the debate on constructing a constitution for Europe. He could seriously tackle the lack of accountability in European decision- making, by bringing new ideas for greater oversight by national parliaments and the European Parliament, as well as exploring devolution of powers to regions. Blair could also take a lead in ensuring that the absorption of new member states from the east brings results which are constructive and not chaotic.
Turning Britain from Europe's pariah into Europe's partner will demand not just vision about Europe's future, but an ability to shift British attitudes, too. The public have been left confused and scarred by the Conservatives' battles with Europe, and education about the benefits as well as the problems is needed more than ever.
In the end, however, if Blair is to stand a chance of making his voice heard on the Continent, he will have to sign up to the single currency, either at the launch or very soon after. Perhaps only when Britain is part of the new reality of European economic and monetary union - the biggest step ever taken on the Continent towards irrevocable unity - will Britain's old historical reflex to divide Europe be tamed, allowing a British prime minister a chance to lead.