One of Madame Tussauds' exhibits has escaped. Eyewitnesses described a waxen, gaunt figure running in the direction of Westminster.

It had a yellowing, snaggled grin, a wispy top-knot for a fringe and a troublingly bulbous left eyeball.

When interviewed, it responded in the husky timbre of a slippered gent who has reached Shakespeare's 'piping and whistling' stage of life.

There is no easy way of imparting this news, ladies and gentlemen. Sir Tony Blair is back. Lock yer doors!

But maybe we should not be so alarmed. The former Labour prime minister, who left Downing Street 19 years ago, wrote a 5,000-word essay about his party's current leadership tussles and Britain's political problems.

How, he wondered, could we prevent our country dropping out of the premier league of nations? Among other things, how should a future government repair the economy and respond to the 21st century industrial revolution of AI?

Awkwardly, both for Leftists who scorn 'Tony Bliar' and indeed for those of us on the Right who have long enjoyed goosing Sir Tony and his grisly galere, his article was strikingly sensible.

He attacked tax rises and welfare hikes. He saw little sense in rejoining an over-regulated European Union (reversing Brexit 'isn't the answer'). 

He praised our alliance with the United States and spoke of Donald Trump with good-humoured amazement rather than bile. The Trump presidency was likely 'a rupture not a reckoning'.

Sir Tony thought we should spend more on defence and we should liberate entrepreneurial spirits. Bridget Phillipson, that frightful sourpuss of an Education Secretary, should stop undoing the school improvements of recent decades. Ed Miliband's Net Zero obsession was crazy. And the government should do 'whatever it takes' to stop illegal immigration.

The essay was so spot-on that Sir Tony was promptly rebuked by Andy Burnham from the doorsteps of the Makerfield by-election. Mr Burnham raged that his former boss did not understand the 'cost of living' problem. More socialism was the answer, argued man-of-the-people Andy.

Meanwhile Labour's other leadership hopeful, Wes Streeting, clutched his pearls that Sir Tony had not mentioned inequality. That was 'the striking weakness at the heart of his intervention', thought pipsqueak Wes.

Some people became a little carried away by Sir Tony's mini manifesto. The Unherd website jauntily imagined his motorcade delivering him to the door of 10 Downing Street where, silky hair shimmering in the summer light, he paused to offer the cameras a soundbite – 'a new dawn has broken, has it not?' – before entering to take over as PM.

Back in real life, mercifully, Radio 4's Nick Robinson asked Sir Tony if he wished he had emulated France's Emmanuel Macron in starting a new party to regain power, and Sir Tony said no.

Phew. We are spared a reprise of Alastair Campbell doing his Basil Fawlty goosesteps through Whitehall's press offices.

But Sir Tony is only 73. He has made his fortune (don't ask how – it was not entirely pretty) and his children are launched. He plainly still worries about the future of his country. 

Can this civic-minded soul, fretting in his high-backed armchair like some retired lad in a Yellow Pages advert, not be put to good use by one of our political parties?

The warmest response to his essay came, notably, from Kemi Badenoch. The Conservative leader wrote an open letter that began with a coy 'Dear Tony (if I may)' and expressed sympathetic regret that the Starmer government has abandoned Blairite policies on trade union law, education and tax.

She regretted that today's Labour MPs do not understand, as Sir Tony's team did, that capitalism and free markets are essential to an economy. She disagreed with Sir Tony over his Human Rights Act and his creation of the Supreme Court, but he was right that politicians should solve problems by working from facts rather than dogma.

'Well, Tony,' she concluded, 'surely now you must accept that the facts of life are Conservative.'

He possibly always did. A solicitor friend of mine, Jeremy Leasor, met the young barrister Blair at a London drinks party in around 1976.

Blair expressed parliamentary ambitions. Leasor wondered which party he supported. Blair replied that he would favour whichever offered him the best opportunities.

It was, in its way, an admirably free-market response. Now Sir Tony argues for a 'radical centre' and believes that the centre ground is under-represented. Is he correct? Is Kemi Badenoch not radically Centrist?

She is pretty sulphurous about the overblown state and has no time for wokery, but these are no longer extremist positions.

She has offered to work on a cross-party basis with Sir Keir Starmer to identify welfare savings. Sir Tony's essay urged Sir Keir to accept this olive branch.

In parliament she has also complimented the Home Secretary, Shabana Mahmood, for trying to get to grips with illegal immigration. Although Ms Mahmood is hated by the Labour Left, most reasonable people on the Right can see she 'gets' the political urgency of stopping the small boats.

If you compare Sir Tony's essay and Mrs Badenoch's current policies, they barely differ. She and he may disagree on the Human Rights Act but they are as one on business, defence, foreign affairs (particularly Israel), energy, employment rights, AI and the aforementioned small boats.

Blair is possibly more Thatcherite on pensions, being sceptical of the pensions triple lock. Mrs Badenoch might yet have to concede that point in order to balance her budgets. She, meanwhile, wants to leave the European Convention on Human Rights. Sir Tony could possibly live with that. Has he not, after all, said we must do 'whatever it takes' to stop the small boats?

They both think Ed Miliband is a nutter, both see Sir Keir is a dud, both think young Wes needs earlier bedtimes.

The Conservatives may lose their deposit in Makerfield but Mrs Badenoch should not be too shaken by that. She understands, as does Sir Tony, that Centrist voters disappear in local elections and by-elections but come out for general elections.

If Mr Burnham becomes PM, Labour at the next general election will offer Corbynism in a black Mancunian T-shirt.

Given Sir Tony's contempt for Ed Miliband, his horror at Bridget Phillipson and his simple bafflement at Angela Rayner's prominence, it is hard to see him seriously campaigning for Labour at that election.

If my friend Jeremy Leasor bumped into him at another drinks party and asked that same question he put half a century ago, logic suggests there could be only one answer: Sir Tony would wear a blue rosette.

Political convention will naturally never allow him to say so in public but we can all see it. Kemi should therefore give the goaty old waxwork a bell and invite him to become one of her advisers.

We need never be told, but she, her party and the country might be the better for it.