How Britain resolves — or fails to resolve — Brexit and the terms of its divorce from Europe, is of more than passing interest to Australia.

It is a bit like watching a loved grandparent in physical and mental decline. You care for them deeply. You appreciate all they have done for you. But each day they become more inwardly focused. Their world contracts. They seem increasingly incoherent.

Britain has a special place in more than just our history. We still share a head of state and with more than 1.2 million of us having been born in the UK, Australia hosts the largest number of British expatriates.

In 1963 then Prime Minister Robert Menzies famously used the words of 17th century poet Thomas Ford in praise of Queen Elizabeth: "I did but see her passing by, and yet I love her till I die". Less formally, Scott Morrison clambering up the Sydney Harbour Bridge in his baseball cap with Prince Harry is perhaps the modern equivalent.

Prime Minister Scott Morrison (far right) and Prince Harry (second from right) climb the Sydney Harbour Bridge ( ABC News )

The ties remain strong, though they are weaker than they were. And like any long-term relationship, they continue to change and develop.

Already, for the past two-and-a-half years since the 2016 Brexit referendum, Britain's national attention and energy has been sucked into the European question.

We're no longer the apprentice

With the UK Government preoccupied with their self-imposed Brexit headache for the foreseeable future, perhaps it is time for the Australian-British relationship to further mature.

It is a time to appreciate that Britain has as much to learn from Australia as we do from them.

Although British political leaders may be less forthcoming, many working on public policy in Whitehall appreciate the enormous amount that can be learnt from Australia.

This amounts to more than being envious of Australia's 27 years of unbroken economic growth.

During my time working in Downing Street, Australian policy experience was enormously useful when British officials considered major policy.

In addressing pensions reform British public servants would marvel at how Australia had achieved a compulsory system of superannuation support for Australian employees, paid for largely by employers.

British policy makers marvel at Australia's ability to implement signficant national infrastructure investment ( Supplied: NBN Co )

Even though Australia has dispensed with four elected Prime Ministers since 2010 — a fact that my former colleagues observe with the same incredulity that we do Brexit — our governments have still worked to establish the National Disability Insurance Scheme and the National Broadband Network. These policies may not be perfect, but despite the apparent "cabaret" of Federal politics, they demonstrate our ability to implement significant social policy reform and national infrastructure investment.

British policy makers — when it comes to policy approaches — are increasingly looking to Australia.

Brexit may weaken trade with Britain

Theresa May has tried to argue that Brexit is not Britain looking in on itself, but looking past Europe to develop "a bold new positive role for ourselves in the world".

So far this is a hard argument to sustain, with her government almost exclusively focussed on the exit deal.

Notwithstanding the stated desire for both countries to negotiate a free trade agreement, work on this cannot commence until Britain has resolved the terms of its departure from the European Union (EU). And with the March 29 "Brexit deadline" looking soft, we could be waiting a while yet.

The prospect is that when it comes to Australian exports, rather than strengthening trade ties to Britain, Brexit could weaken them.

Britain is Australia's fifth largest trading partner — our major exports to the UK are gold and lead (accounting for more than $3.6 billion annually), followed by $413 million of wine exports.

Wine is one of Australia's largest British exports ( Gary Rivett: ABC News )

But what these statistics fail to reveal is that the value of us trading with Britain is greatly enhanced by it being a member of the EU.

Much of the value of Britain as a trading partner to Australian firms is that it is an English-speaking gateway to accessing the far larger €14,800 billion European market.

So if Britain leaves the single market, it may prove easier for Australian firms to bypass the UK and trade directly with the individual EU countries where our goods are sold.

A British or Australian head of state?

The lessons people choose to draw from Brexit could either strengthen the case for an Australian head of state or weaken it.

Twenty years ago, the republic referendum loss meant that the air well and truly went out of the republican balloon. Not a hiss, but a pop leaving the balloon so damaged and bereft of air that not even Malcolm Turnbull as prime minister had any appetite to revive it.

Yet this is about to change. With a Federal election likely in May and Labor committed to holding a plebiscite on the threshold question — "Do you support an Australian republic with an Australian head of state?" — followed by a referendum on the model, the debate over enduring constitutional ties with Britain will surface again in the campaign and, if Labor wins, beyond it.

Most obviously the case for a republic may be bolstered by Britain's fixation with the European question, providing Australia with further evidence of how outdated it is to retain a head of state from another, far distant, otherwise pre-occupied country. Alternatively, in uncertain times, Australians might observe that even though the European question has divided the United Kingdom, perhaps more than anything else it is the constitutional monarchy that has helped maintain some sense of steadiness and durability.

Will Brexit revive calls for an Australian republic?: ( ABC News: Tony Trung )

No matter how unpredictable the UK Parliament appears, how many Cabinet ministers leave, how reactive and agitated the public service is, the argument goes that at least the constitutional monarchy provides some semblance of stability and continuity.

And achieving Brexit has proved a hard enough job for a Prime Minister of a minority government, trying to lead a deeply divided Conservative Party, with a stream of Cabinet resignations, enduring a party leadership challenge, and the worst defeat in British Parliamentary history.

With Brexit making so much in Britain politically and nationally "out of the ordinary", Australians may ask whether the further complication of an elected president would have made decision making any easier for Britain. Surely it would only provide another platform for an ego driven populist to present simplistic answers to complex challenges: would the prospect of President Farage or Johnson help or hinder public decision making?

And, likewise, would an elected head of state here make our capacity to make political decisions in the national interest any clearer?

Citing the example of Brexit could give those against an Australian republic and head of state further confidence in asserting that if it isn't broken, why go through the angst of fixing our "unbroken" constitutional arrangements?

China accounts for more than a quarter of our exports ( Reuters: Jason Lee )

Time to concentrate on new friendships

Despite our historical and cultural links to Britain, Brexit will further amplify the case that Australia's future lies not in our established ties to the UK, but in strengthening the new economic, diplomatic and political relationships in our region.

Our ties to Britain stretch back to white settlement.

Our British grandparent remains loved, but they are not as important to us as they once were.

Now we have younger friends. We may not have known them for as long. And they might not have affected us as much.

But with China already accounting for more than a quarter of our exports, Indonesia having just signed a free trade agreement with us and destined to become the seventh largest economy in the world by 2030, ever more clearly these are the relationships that Australia must focus on and develop to enhance our economy and position in the world.

Nick Rowley was an advisor to former UK prime minister Tony Blair and worked at Downing Street between 2004 and 2006.