The word "historic" is overworked and much-abused in connection with the Northern Ireland peace process. Yet it provides the only adequate description for today's Downing Street encounter between the British Prime Minister, Mr Tony Blair, and the Sinn Fein president, Mr Gerry Adams.

Number 10, predictably if somewhat disingenuously, has been playing down the significance of the event. New Labour's famed presentational skills have certainly been in evidence - smartly avoiding the build-up of press speculation by announcing the date well in advance, and characterising the meeting as one in the Prime Minister's ongoing round of discussions with all the party leaders.

Mr Blair and the Northern Secretary, Dr Mo Mowlam, have established the line by constant repetition: that for as long as the IRA ceasefire holds, and Sinn Fein adheres to the Mitchell principles of democracy and non-violence, the party should be treated on the same basis as all the other participants in the process.

It is little-disputed save by what remains of the "Tory press" and a Conservative front-bench team which appears eager to break the "bipartisan" approach at the earliest possible date. In a bow to the new realism, Mr David Trimble - while voicing just enough criticism to cover his flank - has been more concerned with what Mr Blair should tell the Sinn Fein delegation when they meet, than with arguing convincingly that the meeting should not take place.

Mr Adams has also affected a modest approach, insisting the location is of less importance than the "engagement" he hopes to establish with the British Premier.

However, each side will be acutely aware of the significance of Sinn Fein's acceptance in the seat of British political power.

And while the British won't be so vulgar as to mention it, each side will also be conscious of the parallels being drawn with that earlier visit to Downing Street by one Michael Collins.

Mr Adams was quick to reject any such parallel following the first IRA ceasefire when he observed that Collins had not secured the end of partition. And in the build-up to today's meeting, the Sinn Fein leader has declared himself about concluding "the unfinished business" of Irish unity.

Mr Blair understands that Mr Adams has to say this. But the British hope is that the affirmation of the enduring republican goal is one half of a ritual - matched by a reiteration of Mr Blair's commitment to the "consent" principle - which can be quickly dispensed with.

For the British Prime Minister is not about the end of history. His focus is most emphatically on the "here and now" and on the elements of a political agreement he believes could, and should, be on the table by May. As the dogs in the street know, that agreement presupposes a new power-sharing administration in the North; new structures for North/South co-operation; and a redefined Anglo-Irish Agreement within an enlarged East/West framework.

We also know, from Mr Blair's speech of May 16th, that he considers amendment to Articles 2 and 3 of the Irish Constitution essential to securing an agreement which, in his view, will leave Northern Ireland still an integral part of the UK.

That said, Mr Blair's approach is unlikely to be in any way confrontational. The key for London is to establish a relationship with the Sinn Fein leadership and "the beginning of an understanding" that Mr Blair is serious about political change.

Invoking the "modernising" theme of the Blair administration, sources say the Prime Minister came to power passionately determined that, as far as Northern Ireland was concerned, "things couldn't go on as they were and that we have to find a way of dealing with history".

In that spirit, Mr Blair is expected to emphasise his government's commitment to genuine negotiations; to radical reform and the creation of a fair and equal society; and to secure a settlement, whether or not the present talks process yields agreement.

London understands the difficulty presented by the UUP's continuing refusal to engage directly with Sinn Fein and has privately urged Mr Trimble to find a way over that hurdle. But Mr Blair will probably maintain that the more important consideration is that the key issues are beginning to be addressed.

Mr Blair is likely to stress his commitment to further "prudent" changes in the disposition of the security forces, consistent with the perceived level of threat from elements not committed to the process. And he will point to the progress already made on prisoner repatriations as evidence of his government's good intent.

However, Mr Blair is unlikely to hold out any prospect of prisoner releases in advance of a political agreement and the establishment of a permanent peace. While such moves in the longer term are not ruled out, Irish sources last night confirmed that this issue was not, at present, on the "radar" of either government and that "the dynamic of a settlement" would almost certainly be required to bring about radical change on that front.

On the issue of Britain's sovereign claim, the Irish Government's hope is that Mr Blair will point to the language of the Downing Street Declaration and the certainty that any new deal would incorporate the assurance that Britain would place no impediment in the way of unity should the people, North and South, vote for it in separate and concurrent referendums.

However, there is no doubt in either capital that Mr Blair "will be honest" and straightforward about his commitment to the principles of consent and sufficient consensus.

He is likely to remind Sinn Fein that "all hangs on its commitment to peace and democracy" and of the cost to it should that commitment be abandoned at some future point.

All of which, in the official British mind, translates into the critical question of good faith: will Sinn Fein live with the outcome of the process even if it falls far short of what it wants?

The dominant and prevailing belief in London is that Mr Adams and Mr Martin McGuinness are genuinely engaged and must have "factored in" the likely parameters of any achievable settlement when they began the republican transition.

It is emphasised that, in contrast with the Major government, Mr Blair's is not in the business of inventing new "tests" for the republican leaders. And while it is understood that the crucial period from January to May will prove particularly testing for them, it is observed that "they've constructed it themselves".

In blunt terms, as one source puts it, they've got the inclusive process they asked for. "Up to now they've been able to talk a good game, now they've got to play it."

By which assessment, today's historic meeting could prove more uncomfortable for Mr Adams than for his host.