THE scale and depth of Labour's victory will greatly facilitate the task it faces of putting Britain's relations with Europe on a new footing. Mr Blair has promised to bring his party to the heart of Europe by asserting a new leadership role in its affairs.
But first he will have to repair the political and psychological damage that has been done by years of Conservative Euro scepticism, reinforced during the campaign by Mr Blair's "me-tooism" in tracking his opponents policies.
Labour will also have to determine rapidly what direction it wishes to travel in and how it can best play to British strengths in order to open up the possibility of playing a real leadership role.
There was palpable good will across the other EU member states yesterday, as other governments realised that Mr Blair's victory should allow the Inter Governmental Conference to finish on time. From July, Britain will join the Troika, while in January 1998 it will itself assume the presidency.
In that time, the Labour government will preside over crucial decisions on which states will join the single currency, the opening of enlargement negotiations with central and eastern European states, and intense discussions on new budgetary arrangements.
Britain has major interests in these issues. It will be difficult for a Labour government to maintain a disinterested stance on some of them, as is required for an effective presidency. And it will be essential that it rapidly makes its own position clear on such matters as the single currency.
For how long will it wait and see whether to join? How rapidly will it realise that not to join in a project with which most other states are engaging may open up a prospect of marginalisation that contradicts its leadership pretensions?
If, on the other hand, the EMU project stumbles, a Labour government would have to be highly sensitive to the consequences of failure and the need not to be seen as having encouraged it. This would raise suspicions in France and Germany that British fears that the single currency is the wrong answer to the end of the Cold War had been carried over into an effort to make it fail.
This may seem farfetched, but it opens up the central question of how best Britain can act as a balancing force against the Franco German alliance, which has so far dominated European integration. The smaller states, Ireland included, share an interest in seeing France and Germany balanced by a more engaged Britain. They will be seeking to persuade it to provide that balance in the coming months.
Mr Blair's sweeping mandate, the comprehensive defeat he has inflicted on the Conservatives, the strong performances of the Liberal Democrats and the Scottish and Welsh nationalists mean that he has far more freedom of manoeuvre on Europe than his cautious conduct of the election campaign would lead one to believe.
The issue of sovereignty is central the sovereignty of parliament, of the United Kingdom as a nation state of Northern Ireland and of the UK within a more closely integrated Europe.
Given his commitments to devolution and constitutional reform, Mr Blair will have little option but to manage these issues in a comprehensive and coherent fashion. In that case he should find that progress on one will reinforce progress on the others, creating its own momentum.
That may be an optimistic scenario, but it has been made more likely by this famous Labour victory and the above mentioned flanking effects. From the Irish point of view it seems unmistakably good news. It promises a relationship between political change in Northern Ireland and in the UK as a whole. It also makes it more likely that Britain will closely shadow the first wave of a single currency bloc rather than seek, Hong Kong style, to compete against it by competitive devaluation.
Decisions taken at Amsterdam next month on flexibility will immediately confront the new British government with strategic choices along these lines. The more it opts to wait and see the more the other states will be tempted to create the conditions within which a core group could move ahead of a reluctant Britain. The more Mr Blair demonstrates that he wants to assert British leadership the less likely is that wish to be fulfilled.
His relationship with Germany will be crucial, following the drastic deterioration of recent years and the xenophobia of the British right. It will be interesting to see, too, how his victory pans out, through other social democratic parties in the EU. It was being seen yesterday very much as a political event with relevance to Europe as a whole, and not only to Britain.
Socialists in France, Italy and Germany may draw inspiration from it to formulate an alternative approach towards the single currency criteria, which are being criticised more and more by the left in these countries as "neo liberal".
In this perspective, the forthcoming French election will be crucial. Were it to result in a parliamentary majority for the Socialists, Communists and Greens we could see the emergence of an alternative axis for a British Labour government to relate to.
In an interdependent world, political energy flows across borders rapidly and with unanticipated consequences. The international political fallout from Labour's victory will take weeks and months to settle. Interesting times, indeed.