He must hope that it will lend him luck as well as gravitas, for he knows all too well what followed that last encounter. The treaty Collins signed with Lloyd George led to a bloody civil war, his own death, the partition of Ireland and decades of bitterness.
Three-quarters of a century on, a few members have already resigned from Sinn Fein and the IRA, suspecting that Adams may, like Collins, be prepared to settle for less than the hallowed republican goal of a united Ireland.
Gerry Adams, asked about the state of play within republicanism, gives a relaxed shrug: "Think of the IRA as a corporate organisation. People leave all the time, people come in all the time, people have rows all the time, people die, take career breaks and so on.
"So one, two, three people leave; presumably they are replaced and the organisation goes on because the IRA is bigger than any grouping of people. There was certainly a mixing [stirring] and putting out disinformation by the securocrat community. This got expanded out of all proportion but as far as I'm concerned it's a dead story."
The same people, he says, may have been behind last week's stories that he is a member of the IRA's army council, which he denies. Who are these 'securocrats'? "Whether it's the London civil servant who coordinates security, or the head or the RUC or the British generals, or whether it's the people in MI5 or MI6 who don't have another pot to stir, there are people who want to stick with the old security agenda rather than move to a new political agenda.
"One question that's very much on people's minds here is Bloody Sunday. Everybody knows it was a premeditated attack as part of the military-political strategy at that time. You'd think it would be relatively easy to set up an independent inquiry to sort everything out, but to do that means the Prime Minister has to challenge all that stuff. That's the test."
The other opponents of change, he claims, are the Ulster Unionists. At the Stormont multi-party talks he congregates with other party leaders including David Trimble, but the Unionists will not negotiate with Sinn Fein or openly speak to them.
According to Adams: "We're meeting in a room twice the size of your average living-room so you can see the whites of people's eyes. Outside the room the odd one will say 'Hiya' or smile. It can be bizarre and surreal because then when you meet someone in the men's room you've a captive audience so you can banter for two or three minutes.
"David Trimble is a case apart because David pirouettes at the sight of a Sinn Fein person. And it's not just us: the Unionists don't engage with anybody. I've heard them, in fact, being even more vitriolic about the British government than with Sinn Fein. I do understand that they have huge difficulties but this doesn't show a vision for the future. It's minimalist, it's begrudging, it's nagging, it's negative."
Adams has already met Tony Blair in Belfast for a meeting which he describes as a good start. He is hopeful of building a relationship: "I've only met the man once but he certainly impressed me that he had a better grasp of the issue than newspaper pundits and others may have given him credit for.
"You don't get to be leader of the Labour Party and get into government if you are a Bambi. You have to be tough, you have to be informed, you have to have ambition, you have to have a political vision. I think he clearly has all of those and he understands the Anglo-Irish situation better than one would presume. I just don't know how much he understands it.
"He does know there has to be change in this situation: the question is how much change. We're talking about a British prime minister, whether he ever says it or not, being prepared to bring about an entirely new relationship between these two islands based upon mutual independence and respect. From our point of view we're talking about maximum change, we're talking about a total transformation."
Everyone knows, however, that when the talks reach their deadline of May next year they will not produce a united Ireland. So what happens if the result is an arrangement which, though far-reaching, falls short of the Republican dream? The Sinn Fein President's response may be taken to imply that it might not have to be all or nothing.
"What we will do when it comes to the point where there is a conclusion, whether in May or before it or after it, is draw breath," he says. "I think the most honest answer you can give is to say, 'Let's go for agreement, let's go for a democratic settlement and when that's visible then we can judge that on its merits.' We will see the shape of the deal, we will take a democratic judgement on it within the party and then pursue the outcome of that.
"I see this as a phase, and we obviously want to go as far as we can in this phase. If there is not a united Ireland coming out of this process that doesn't mean that the pursuit of a united Ireland isn't going to continue after this process, because it is."
These words carry an eerie echo of Michael Collins, who argued that in signing the treaty he had not won freedom but had won the means to achieve freedom. When Gerry Adams walks through the doorway of Number 10 this week his coat may be new but many of the issues, and the dangers, remain unchanged.Reuse content