Within months, however, a nightmare scenario had begun to appear on Downing Street's radar screen. Far from killing off the Scottish National Party's demands for independence, had the Government merely played into its hands by allowing the separatist genie to come out of the bottle?
Mr Blair, never a passionate advocate of devolution, wondered whether he had made a catastrophic error that could lead to the break up of the United Kingdom.
The answer will become clearer on 6 May, when the first elections to the new Parliament in Edinburgh take place. Although Labour's nerves have steadied since last year's Scottish National Party (SNP) opinion poll advance, it is no exaggeration to say that the future of the UK is at stake. This is why the elections to the Scottish and Welsh assemblies matter to people in England, too.
Even if, as the opinion polls suggest, Labour emerges as the largest party in the Scottish Parliament, the SNP can expect to form a sizeable opposition with a powerful platform from which to pursue its aims.
Plenty of Labour MPs privately share the view of Alex Salmond, the SNP leader, that it is now only a matter of "when" rather than "if" Scotland votes for independence in the SNP's long-promised referendum.
Whatever the results next month, the elections in Scotland and Wales will have far-reaching consequences for British politics. Ministers believe the creation of the new assemblies will sooner or later fuel demands for elected assemblies in England.
A strong showing for the SNP, and the prospect of a breakaway, might well harm the career prospects of the six Scots in the Cabinet, and dash Gordon Brown's hopes of succeeding Mr Blair as Prime Minister.
Mr Salmond describes himself as "Gordon Brown's nemesis" and it is no wonder the Chancellor is calling the shots in Labour's campaign: he has installed key aides in Scotland and when he is stuck in London, he holds a telephone conference call every morning with the party's campaign headquarters.
The heated debate in Scotland over tax, with the SNP proposing to reject Mr Brown's 1p cut in the basic rate next year, will tell us whether the Scots are prepared to put their money where their mouths are to preserve public services.
The Scottish poll will also provide an insight into public opinion on the Kosovo crisis. So far, Mr Salmond's condemnation of Nato's strategy appears to have backfired, but events in the Balkans could yet change that.
The elections will be the first in Britain fought under proportional representation (PR). Whether the voters like the system could help determine whether it is introduced for the House of Commons. First, though, they will have to understand it. "It must be the craziest system in the world," one Downing Street aide moaned last week.
People in Scotland and Wales will have two votes - one for a candidate in their Westminster parliamentary constituency, and one on a party list in their region. There is nothing to stop people casting their two votes for different parties, and surveys have suggested one in three may do so - which should boost the nationalists.
The Scottish Parliament will have 129 members, 73 representing individual constituencies, elected under the first-past-the-post system, and 56 from party lists in Scotland's eight regions under a proportional "topping up" process.
Opinion polls since the campaign began two weeks ago have shown a Labour advance and an SNP decline, raising Labour's hopes of winning an overall majority. But this looks unlikely; although Labour holds 56 of the 72 Scottish seats at Westminster, it has never won more than 50 per cent of the votes in a general election. So the most likely outcome is a Labour- Liberal Democrat coalition.
Wales will use the same method of voting: the Welsh Assembly in Cardiff will have 60 members, 40 elected in each of the principality's Westminster seats by first-past-the-post and 20 from the five regions in Wales under the "topping up" process.
The byzantine nature of the system is best illustrated in Wales, where it could deprive Alun Michael, the Secretary of State for Wales and Mr Blair's candidate to become First Secretary, of a seat, because he is standing for a "top-up" seat rather than a constituency.
Perversely, if Labour does well in the constituencies in Mid and West Wales, Mr Michael may not win. Labour's polling experts put Mr Michael's chances at no better than 60-40. If he loses, Mr Blair will suffer the embarrassment of having to endorse Rhodri Morgan, the independent-minded MP for Cardiff West whom he moved heaven and earth to block, as the Assembly's Labour leader.
But Labour's prospects in Wales are better than in Scotland. The party should win an overall majority and would do so if it repeated its performance at the last two general elections (even though it failed to land a majority of the votes cast in 1992).
Allowing people to have two votes might help Plaid Cymru to push the Tories into third place in the Assembly. In contrast to their sister party in Scotland, the Welsh nationalists do not advocate independence from the UK.
The battle for Wales is also different because the Assembly in Cardiff will enjoy much less power than the law-making Scottish Parliament. It will be limited to detailed "secondary legislation" in line with that already passed by London. Although there is less demand for devolution in Wales than Scotland, the nationalists hope the "glorified talking shop" being opened this year will prove a stepping stone to a Scottish-style parliament with real clout.
SCOTLAND: KEY ISSUES
Should the Scottish Parliament be a "bridge" to independence; whether to use new powers to vary income tax by up to 3p in the pounds ; sense of nationhood; can coalition government work; knock-on effects for England; will minority parties, particularly hard left and the Greens, benefit from new PR-style voting system?; party leaderships, particularly SNP's Alex Salmond for "unpardonable folly" remarks about bombing Serbia.
Linlithgow, marginal seat held by maverick MP Tam Dalyell; Glasgow Govan, shipyard closure could hit Labour; Ross, Skye and Inverness West, Charles Kennedy must deliver to help his Liberal Democrat leadership bid; Falkirk West, renegade Labour MP Dennis Canavan standing as Independent; Edinburgh South, former SNP MP Margo MacDonald (above), thorn in Alex Salmond's side, likely to win seat; Perth, Tory revival could harm SNP MP Roseanna Cunningham.
Donald Dewar, dour Secretary of State for Scotland; Alex Salmond, garrulous SNP leader; Tommy Sheridan, poll-tax convict, leader Scottish Socialist Party; Sean Connery, SNP supporter and actor (right); Donnie Munro, former member of Runrig folk/rock group; Lorraine Mann, standing for new Highlands and Islands Alliance; EastEnders' Ross Kemp, swapping Albert Square for Sauchiehall Street; Alex Ferguson, if Manchester United start losing.
HOW THE VOTING SYSTEM WILL WORK
These are the first elections in Britain to be fought under a system of proportional representation, the aim being to ensure each party receives the number of seats which reflects the level of support among the voters. Each elector will have two votes. The first will be cast for a candidate to be elected on the first-past-the-post principle in existing constituencies for the Westminster Parliament. The second will be castunder the Additional Member System (AMS), so parties which polled well but did not win the constituency vote can still be represented. It is expected that parties will need at least 6-7 per cent of the vote to have any chance of winning seats under AMS. In Scotland, 73 MSPs will be elected from constituencies and 56 from party lists in eight regions. In Wales, 40 members of the Assembly will come from the constituencies and 20 from lists in five regions.
WALES: KEY ISSUES
Labour splits over Alun Michael as New Labour choice as First Minister; the extent of Plaid Cymru's commitment to independent Wales, or "national status within Europe"; do Welsh feel more Welsh than British?; NHS and waiting list concerns; will the assembly be only a glorified county council? right-wing Welsh Tory leader Rod Richards at odds with more left-leaning senior party figures; turnout amid voter apathy.
Mid-Wales where Alun Michael (right), Blair's choice for First Minister, is trying to win from the "top-up" list; Caerphilly, where Ron Davies is staging a comeback; Cardiff Central, Labour seat and key target for Lib Dems; Monmouth, Labour/ Tory marginal, only black candidate - Labour's Cherry Short - is standing; Clwyd West, where Tory leader Rod Richards, is trying to get back into frontline politics. Ynys Mon, Plaid Cymru's most vulnerable seat to Labour.
Alun Michael, Welshman parachuted in by New Labour Englishmen; Rhodri Morgan, loose cannon not on Tony's Xmascard list; Ron Davies, post Clapham Common; Rod Richards, abrasive Tory leader and no Hague man; Dafydd Wigley, Plaid Cymru, president; Alison Halford, ex-Merseyside police chief standing in North-east Wales; Cerys Matthews (above), Welsh-speaking leader of Catatonia, may hit the hustings; weatherwoman Sian Lloyd, who might stand next time, but not sure who for.