Following a discussion in Washington with President Bill Clinton last week it was agreed that the issue should be put on the formal agenda for the next summit of the G8 most important industrialised countries, in Birmingham, in May.
Contingency planning is underway in Whitehall to protect against breakdown in key industries like gas, electricity, water, railways, broadcasting and telecommunications.
The Prime Minister has agreed with Wim Kok, the Dutch Prime Minister, that Britain should stage "a round table conference of senior industry figures" from Europe, also expected in May.
The crisis will strike home on New Year's Day 2000 because millions of interlinked computers, across the world, are programmed to "think" that the year 00 means 1900. The problem will be compounded by the fact that programmes are riddled with inconsistent reactions. One programme is reported to accept 00 to 29 as 2000 to 2029, but when 30 is offered, it reverts to 1930. A breakdown in one critical system can trigger an infinite domino effect, with unknown consequences.
In an appeal for a British lead, Mr Kok has warned the Prime Minister: "The chain is as strong as its weakest link, at national as well as international level."
Mr Blair replied: "I am convinced that the problem is larger and more urgent than many people realise, but if organisations act today there should still be time to deal with it."
But the Prime Minister warned: "There is a growing shortage of skilled people and governments and businesses will need to think hard about priorities."
A No 10 source has told The Independent that the a new Cabinet committee, chaired by Margaret Beckett, President of the Board of Trade, would "focus particularly on infrastructure" - ensuring that contingency plans are in place. Mr Blair's campaign to create an impetus for action has been stimulated by apocalyptic warnings. One source close to the Prime Minister said last week that the "bug" could knock 2 per cent off the national income of all G8 countries in 2000: a pounds 250bn bombshell.
That warning has been tracked back to Wall Street guru Edward Yardeni, chief economist for Deutsche Morgan Grenfell, the investment bank, which gave evidence to a Senate hearing last November.
"Based on what I know so far," he told the hearing, "I believe there is a 40 per cent risk of a world-wide recession that will last at least 12 months starting in January 2000, and it could be as severe as the 1973- 74 global recession.
A survey by PA Consulting reported that only 55 per cent of UK companies were fully aware of the implications of the "bug", and it is thought that only 20 per cent of small to medium-sized companies are up to scratch. "This sector may have serious difficulty in operating through the millennium," a No 10 source said.
Robin Guenier, the head of Taskforce 2000, which was set up with limited finance by the last Government, said yesterday: "This is a major threat to the British economy. Even though the levels of awareness in the UK are higher than anywhere else - the level of action is inadequate."
He said that while BT had made reasonable progress in upgrading its equipment less than half of European and North and South American systems had reached the British level of preparedness, while the proportion for south-east Asia was less than 25 per cent.