In the latest murder a man was shot dead shortly before midnight last night outside his house in Salters Grange, Armagh.
Sir Hugh also warned that the IRA was intent on staging one of its 'spectaculars', either in Northern Ireland or in Britain. His grim assessment was that both republican and loyalists groups show no sign of easing off in their killings.
Three of the last four deaths happened in the Belfast area over a period of 15 hours. The killing by the Irish National Liberation Army of a Protestant on the outskirts of north Belfast was swiftly followed by loyalist killings of two Catholic men. The INLA described its victim, Gerry Evans, a shopkeeper, as a loyalist extremist, but friends said he was a non-political person who did much work for charities.
The first loyalist killing came at Springfield Park, where Ulster Defence Association gunmen apparently crept through a breach caused by builders in a 'peaceline' wall. They opened fire on a car containing two Catholic men, killing Liam Paul Thompson, 25.
His friend Patrick Elley, who was driving the car, was injured in the leg. He survived a hail of bullets which made four holes in his jacket but missed his body. Locals complained that they had warned the RUC the peaceline had been breached.
The other main loyalist terrorist group, the Ulster Volunteer Force, carried out the killing of a Catholic newsagent in the docks area of the city at around 6am yesterday. Jim Brown, a 47-year-old father of three grown-up children, was shot behind the counter of his small shop.
Ronnie Flanagan, Assistant Chief Constable of the RUC, said: 'What we have here is a hardworking absolutely innocent soft target, working in a shop, opening at 5.30 every morning to provide a service to all the community. This morning somebody took advantage of the fact that he was such a soft target and entered his shop and murdered him.'
In a news conference called after the killings, Sir Hugh Annesley said the situation was serious and could get worse, with a significant threat existing in Britain.
Giving his analysis of the IRA's position, Sir Hugh added: 'The peace process clearly continues. It is primarily a matter for politicians, but my personal view is that the Downing Street declaration is unquestionably a watershed, both in security terms and politically, in that it has to some degree forced the IRA into a cul-de-sac.
'I think it leaves the IRA wondering where to go and I have no doubt that that debate within their circles continues.'
The United States has issued a visa to a senior official of Sinn Fein, the political wing of the IRA, the State Department said yesterday. A spokeswoman said the visa had been granted earlier this week to Mitchell McLaughlin, national executive chairman of Sinn Fein, to allow him to fulfil a speaking engagement in Cleveland, Ohio.
Earlier this year, a dispute erupted when Washington allowed Gerry Adams, Sinn Fein leader, to visit the US for 48 hours.