Instead they tried to keep it secret, and now the news has leaked out. You would have thought they might have learnt a couple of lessons from the row last year which followed the disclosure that the British government had been in contact with Sinn Fein officials for two years while insisting in the House of Commons that no such contact had been made.
The lessons? The first is that secret meetings are bound to feed Unionists' worst fears of a secret backroom deal to sell them down the river. The second is that in the hothouse world of Irish politics, secrets can rarely be kept.
That said, it was clearly a good idea for Mayhew and Adams to meet in a private session in which they could talk frankly. For there are surely ways out of the impasse over whether anything else can be done until the IRA agrees to begin decommissioning its arms. The Government is right to say that this will prove the ultimate test of republican good faith. But it has to recognise that crossing such a Rubicon will inevitably be a tough policy for Adams to sell to his movement's hard men - even in the context of the plan for an independent commission to disarm paramilitaries which apparently is being privately proposed by the Irish Foreign Minister, Dick Spring.
Meanwhile there are concessions which the Government could allow to make it easier for Adams to advise the IRA that the time for decommissioning has arrived. The most obvious of these is on prisoners - an area where the Government has moved too slowly, especially in the context of its misjudgement in releasing Private Lee Clegg as a sop to the parliamentary party during the recent leadership election.
There are three steps to be taken. First, the growing tension over the "dirty" protest by five republicans in English jails could be eased by transferring the men to Northern Ireland. Second, when the European Convention on the Transfer of Sentenced Prisoners takes effect in November, significant numbers of terrorists could be transferred to jails in the Irish Republic, subject to the proviso that they are not released precipitately. Third, the Government could act on proposals which have been drawn up by civil servants suggesting that a new parole board be set up in Northern Ireland empowered to release prisoners after they have served only half, rather than two-thirds, of their sentences. Such a move would free another 100 prisoners by Christmas. Releasing them on licence would allow them to be re-imprisoned should violence return or if they were to re-offend.
In addition, Sir Patrick Mayhew should be bold about pursuing the idea he is said to have tentatively advanced with Irish government officials about the gradual disarming of the RUC. Above all, the Government should be undaunted about continuing to be seen to talk openly to Sinn Fein when it can see advantage to the peace process.