Problems are piling up at Mr Blair's door. Real, serious problems - sufficient in subject and scope to suggest opportunity, even, for the Opposition.

Not, of course, that any of the fundamentals of the British political landscape have changed in the first two weeks of this new year. Mr Hague is still the one with an electoral Everest to climb.

Tory insiders privately acknowledge the Hague mission which cannot publicly speak its name - to fare well enough to remain as leader of the Opposition in the next parliament.

Given party rule changes, Mr Hague has made it much more difficult for critics to mount a leadership challenge. However, with the general election believed to be little more than a year away, party strategists say the next few months will be crucial and that, without evidence of some improvement in the Tory leader's personal fortunes, another outbreak of "headless chickenry" cannot be entirely ruled out.

The Prime Minister must give thanks for such hapless opponents. For all his generally applauded performances in the Commons, Mr Hague struggled in vain last week to win advantage as Mr Blair reeled under charges that ministers had exaggerated the extent of the flu "epidemic" in order to mask the underlying weakness of the National Health Service. Indeed, Mr Hague's intended assault ended up with a blistering attack from Mr Blair on his own cost-cutting performances in the health sphere as Secretary of State for Wales.

That said, the crisis in the NHS - coming amid a sea of other troubles - has almost certainly marked a turning point in the experience of the New Labour government, and the nature of its relationship and discourse with the British public.

The evidence of the latest ICM poll is that, especially on health, there is awareness, sophistication, and sheer day-to-day experience "out there" simply not susceptible to the politics of the soundbite - or the increasingly threadbare insistence that everything remains the fault of the last Tory government.

Not all the government's difficulties are so fundamental or challenging, although even the little ones have a way of playing into Mr Blair's "big picture".

From Scotland come renewed signs of strain in post-devolution Britain. The Scottish Executive is reportedly ready to dilute plans to abolish university tuition fees, allegedly under pressure from Whitehall ministers fearful that they could ultimately be obliged to extend a similar deal to students from England, Wales and Northern Ireland at a cost of £700 million.

It remains to be seen how that will affect relationships within the Labour/Liberal Democrat coalition in Scotland, while Labour's hostility to electoral reform inclines increasing numbers of Mr Charles Kennedy's MPs to question the wisdom or benefit of "constructive opposition" at Westminster.

On the wider shores of devolution, meanwhile, Mr Blair faces the real possibility that Mr Ken Livingstone might manage to overcome the resistance of the Old Labour-style electoral college and win the party's nomination for London mayor. Equally troubling for Mr Blair is the alternative scenario in which Mr Livingstone, having demonstrated himself the popular choice of the rank and file, might yet stand against the selected candidate and win.

Jack Straw has not been fatally damaged by a difficult week at the Home Office. On individual issues such as Pinochet, close observers feel Mr Straw has "played it by the book". On the question of Mike Tyson's entry into Britain, the calculation will be that the public cares little about the original insistence that immigration officials would play it similarly by the rules, and have appetite only for the fight.

Yet on a whole succession of issues - from passports to Pinochet and (falling) police numbers - Mr Straw is frequently reminded of the reputation of the Home Office as a potential political graveyard.

With the transport crisis temporarily off the front pages and the flu yet to strike, the year began with cruel mockery of Mr Blair's dome. This is easily overdone. For all the fiasco on the opening night, surveys show a clear majority of those making the trip to Greenwich find the Dome an enjoyable and worthwhile experience.

However, as politicians will be the first to tell you, the general public can be mighty fickle. And as dome headlines gave way to crisis in the NHS, many will have privately endorsed the reported view of Prince Charles that "the monstrous blancmange" was a "crass waste" of £750 million.

The prince's reported views came at the end of a week of battering headlines proclaiming news of a cancer victim who had her operation postponed four times, only finally to be told her condition had become inoperable; of elderly patients being driven around the country in search of intensive care beds; of refrigerated containers being used as temporary morgues; and of NHS patients remortgaging or even selling their homes to beat long hospital waiting lists.

One woman - admitted to a South London hospital with pleurisy and subsequently released before she had fully recovered because "they needed the bed" - told of her amazement at finding two other elderly patients being transferred at 3 a.m. A BBC journalist, a lifelong Labour supporter, tells of helping an elderly neighbour to hospital and fearing he might never see him again.

Real fears about the state of the NHS had bitten deep with the public even before heavyweight commentators weighed in with confirmation that the health service in Poland was better provided for. And while a clearly concerned Mr Blair sought to regain the initiative - pledging an extra £12 billion over six years to tackle "fundamental problems" and bring Britain's health spending up to the EU average - it was unclear if yesterday's headlines would assuage the growing belief that radical health surgery is now called for.

Even if health spending is increased from 6.8 per cent to 8 per cent of Britain's national wealth, this will still be less than in Germany and France. Moreover, Mr Blair - his face set equally against expanding the public-private partnership or raising taxes to meet the mounting bill - makes clear that this is all dependent on the economy continuing to perform well year on year.

Which leads us back to where we began. Mr Blair won the last election in part by persuading middle England that it was safe to make the change: that they could have Labour - and that Labour would make the difference in such areas as transport, education and health - without raising taxes. Since then Conservatives have railed that much of their seeming impotence derives from New Labour's occupation of traditional Tory territory. "You won't solve the problem simply by throwing money at it" has become a familiar Labour refrain. Yet, faced with this crisis, that would appear to be the government's answer.

While mocking Mr Blair's much-vaunted Third Way, Mr Hague has promised radical solutions of his own. And against all the received wisdom that health is inevitably a winning issue for Labour, there may be opportunity here.

Certainly Mr Hague - going nowhere in the polls - might find the British people responsive to a more candid discussion about their health and its cost. He might also benefit by dispelling the impression of a single-focus fixation with their future in Europe.