Dressed in a smart shirt, a bow tie and standing under a portrait of Her Majesty the Queen, Solomon Levy, 80, has a blunt message for Spain.

Key points: Gibraltar under British control since 1704

Gibraltar under British control since 1704 Spain eyeing control after Brexit

Spain eyeing control after Brexit Gibraltar Chief Minister says Spain has 'unhealthy obsession'

"Gibraltar was given to Britain for forever," the former Gibraltar mayor says.

"Emphasis on forever. Not like Hong Kong."

This week Spain issued a formal request for joint sovereignty over the British territory, repeating a demand made on the day Britain voted to "Brexit". Spanish eyes are firmly fixed on taking back control.

Its Foreign Affairs Minister Jose Garcia-Margallo recently insisted that joint sovereignty is "an opportunity to create more wealth in the region".

"Spain wants the best for Gibraltar," he added.

At the Rock of Gibraltar, the locals are not amused — especially with the "unwelcome fixation" shown by Mr Garcia-Margallo.

It is a view shared by Gibraltar Chief Minister Fabian Picardo, who sat down with the ABC recently.

"The Spanish minister has been unhealthily obsessed with Gibraltar from the moment he took over in 2011," he said.

Perched on the southern coast of Spain, Gibraltar is a last outpost of Europe facing Morocco.

Its 30,000 residents, crowded into a seven-square-kilometre enclave, are up against one of the biggest challenges in their extraordinary history.

But residents like Mr Levy are confident the community can stand firm.

"You know the old saying?" Mr Levy asks rhetorically. "Steady as the rock of Gibraltar."

Gibraltar a source of tension between UK and Spain

Taxis line up in the town of Linea de la Frontera to cross into Gibraltar. ( ABC News: Brietta Hague )

In the June Brexit referendum, 96 per cent of Gibraltarians voted to "Remain" part of the EU.

They were fearful of upsetting the status quo, which has allowed both British citizenship and unrestricted trade and travel in Europe.

People openly cried in the streets when they heard news of Brexit's win. Within hours, Spain's Foreign Minister pounced.

"The Spanish flag on the Rock is much closer than before," Mr Garcia-Margallo promised.

Fabian Picardo says the British outpost does not want Spain to take control. ( ABC News: Brietta Hague )

It is a source of major diplomatic tension.

In August, British warships steamed to Gibraltar in what seemed like a show of force, and Britain refuses to negotiate on the Rock's sovereignty.

Spain is stepping up the pressure. Last week, UN ambassador Roman Oyarzun Marchesi argued Britain should agree to joint sovereignty to maintain free movement between the territories.

Spain contends Gibraltar's territorial status violates the UN's core principles on decolonisation.

Mr Picardo dismisses Madrid's rhetoric as "irresponsible," and complains of tighter border controls it has imposed over the last five years.

"All it has brought is hardship, especially to the Spanish people who access Gibraltar on a daily basis," he said.

Twelve thousand people commute across the border for work in Gibraltar's construction and service industries.

EU membership guarantees an open border, but Spain's increased security checks, among other restrictions, has slowed traffic.

It has been described as a "war of attrition".

Spain has done this before. It isolated Gibraltar completely in 1969 when dictator Francisco Franco arbitrarily closed the border, after Britain attempted to establish a constitution in the territory. It took 13 years before it was reopened.

"More than half of our job market comes from across the frontier every day," Mr Picardo said.

"We rely on free movement."

Gibraltar's British touches and Spanish influence

Wild macaques are commonly found at the iconic Rock of Gibraltar. ( ABC News: Brietta Hague )

The Spanish crossing into Gibraltar is from the town of La Linea de la Concepcion, where taxi drivers wilt in the heat waiting to take British tour groups across the desolate no-man's land. Cars can queue for kilometres.

Once across, the first sight is the famous Rock, the jagged, ash-grey promontory that looms above the town.

The view from the Rock of Gibraltar. ( ABC News: Brietta Hague )

Then there are unmistakable British touches; red phone boxes, street lamps and double-decker buses.

But the long history of inter-mingling with Spain is also obvious. Broad cockney accents seamlessly switch into perfect Spanish.

Britain seized Gibraltar in 1704 during Spain's War of Succession, and it was ceded "in perpetuity" under the Treaty of Utrecht. For three centuries, Spain has itched to have it back.

Mr Levy's family history goes back 250 years. His office is hung with huge portraits of both the Queen and Winston Churchill.

The former mayor's reception foyer is a treasure trove of photos, flags, trophies and teddy bears, all celebrating Great Britain.

He said he was excited to meet an Australian, as he was a huge fan of the 1970s television series The Sullivans, which featured a family living through World War II.

"We had it on television here. We all loved it," Mr Levy said.

'We're not worried about Brexit': former mayor

Mr Levy remembered how World War II dramatically changed the lives of the locals. Gibraltar was a strategic base for the Royal Navy, as it is poised at the entrance to the Mediterranean Sea.

Britain evacuated residents for their safety. They had shortly returned when Gibraltar was dealt another blow from Franco's blockade.

"This is why we are not worried about Brexit. As you can see, we've been through hard times before," he said.

In a 2002 referendum, 98 per cent of Gibraltarians voted to remain British.

The question now is whether they can successfully remain a British territory without guaranteed access to the country that surrounds them.

Mr Picardo hopes Spain will realise it has a lot to lose if it restricts free movement.

"One of the main concerns should be the thousands of Spaniards who have jobs here," he said.

But after bristling for three centuries, an emboldened Spain is intently watching Britain's every move towards Brexit.