As the media excoriates the fallen heroes of England's squad after the appalling loss to Iceland at the European Championships and pours scorn on the hapless Roy Hodgson, the search is now on for a new manager.

The qualities of numerous candidates are being extolled – home-grown heroes such as Sam Allardyce, Steve Bruce and even the back-from-disgrace Glenn Hoddle (the man whose views on reincarnation got him into such trouble nearly 20 years ago) – are being touted as men who could make England great again.

Others champion well-credentialled foreigners such as former German coach Juergen Klinsmann, ex-PSG boss Laurent Blanc or Arsene Wenger from Arsenal.

England should look foreign, but surely the answer is obvious: go Australian.

Eddie Jones has transformed English rugby's easybeats and made them one of the top teams in the world in a matter of months following their disastrous Rugby World Cup performances in 2015.

The Australian coach has given the players self-belief, confidence and the wherewithal to take on anyone, as the 3-0 clean sweep of the Test series against the Wallabies proved.

Trevor Bayliss took control of the England cricket team, and immediately got results. The former NSW middle-order batsman took charge when England regained the Ashes in 2015, showing that form to be no fluke when he guided England to a series win in South Africa in 2015-16. He subsequently led England to the final of the Twenty20 World Cup earlier this year as well.

Surely Postecoglou must now be on England's radar, if only on the basis that "if you can't beat them, join them".

Postecoglou might not be as well known in soccer circles as Jones and Bayliss were in their respective sports, but that shouldn't concern a desperate England.

He has shown grit, determination and toughness, and has proved himself tactically astute in grinding out results in World Cup qualifiers and winning the Asian Cup in style at home last year.

The Melburnian is a man who knows his own mind, doesn't suffer fools gladly (handy when dealing with the dazed and confused powerbrokers of the FA), calls a spade a spade, argues his corner and fights fire with fire (handy when dealing with the English media) and is no respecter of big names and reputations (essential when dealing with the misplaced egos of the England squad).

What's not to like?

Of course it would be bad news for Australia, but this nation is used to making sacrifices for the mother country, so another won't really make all that much difference.

Come to think of it, perhaps he could still manage Australia at the same time, taking an overview from London, rather like previous governments did pre-Federation. No reason why not if he can keep trusty sidekick Ante Milicic in charge of the Socceroos while he is away.

And it would certainly make it easier for him to keep an eye on the admittedly dwindling number of Australians playing in Europe's bigger leagues if he was holding the reins for England at the same time.

OK, I admit it's not likely to happen. And knowing Postecoglou, even if he was offered a job of that stature it's unlikely that he would accept, certainly while he feels he still has a job to do with his own national team.

But it's delicious speculation, if nothing else.

For anyone who, like me, grew up watching England and remembering better times – I am old enough to remember, as a nine-year-old, watching Geoff Hurst's hat-trick in the 1966 World Cup final – this was surely a nadir, worse than the embarrassing 1-0 loss to the part-timers of the US.

As if a nation plunged into conflict and already confused, angry and frustrated by last week's Brexit vote had any reason for further despair.

The 2-1 loss to the Nordic minnows must rank as worse even than the 2-1 loss to Norway in 1984, when the Norwegian commentator heaped ignominy on the England team by telling "Maggie Thatcher's boys" that they were not good enough. That was merely a qualifying match, not a knock-out game in a prestigious tournament.

There were no excuses for this disaster. Hodgson's team was simply awful.

The plutocrats of the Premier League were quite simply undone by a bunch of committed, enthusiastic, organised, wholehearted, brave, fit, strong, determined but largely limited players who were able to summon a sense of togetherness, tactical acumen, sharpness and skill to see off an England team that was bereft of imagination, wit, guile or style.

A bloated, preening mass of so-called superstars who once again were found unable to produce a result against inferior opposition when it really mattered.

It is impossible to imagine Italy or Germany slipping up on an Icelandic banana skin. They would simply know how to take care of business.

England, however, just can't.

I watched this game in my 84-year-old father's lounge room in London: we hoped for an interesting and entertaining game, and fully expected England to take an early lead, score a second and "ice" the game.

In the end, so disgusted and frustrated were we with England's performance, that we ended up barracking for Iceland, supporting the underdog in the hope that a loss would perhaps finally lance the boil that is England's complacency.

When the final whistle went and Hodgson resigned post-match – paralleling David Cameron's departure last Friday after the Brexit shock – there was not so much a numb sense of despair but a feeling of anger and contempt.

Hodgson is a decent bloke. I am sure the players are all gutted. But really, what on earth are they doing?

Still, the English Premier League kicks off in six weeks' time, the drama and hype will be cranked into overdrive and the frustration, disappointment, anger and shame of Euro 2016 will be forgotten.

Until the next time ...