Dolphins? Whales? Or just the strange shapes sculpted when a mighty ocean meets the sea where civilisation grew? Luckily, I had clicked my way to a window seat on the flight from Gatwick to Gibraltar, so I spent the final approach to continental Europe’s most remarkable airport trying to sort the marine mammals from mere waves. The Strait here is one of the richest stretches of water in the world in terms of cetaceans, and you can study it in great detail as you come into land.

‘Land’ may not quite be the word for the southernmost airport in mainland Europe. The naval airfield that doubles as the civil airport in Gibraltar extends on either side of the narrow isthmus joining the Iberian peninsula to one of those now-rare pink bits of the map, Britain’s multilayered, multidimensional place in the sun.

If you love to fly, Gibraltar should be top of your list. Besides scanning the sea for cetaceans, you can see two continents: this is the point where Europe and Africa get tantalisingly close. The Strait that separates the two is also a conduit – one of the busiest sea lanes in the world, connecting the Mediterranean with the Atlantic and the rest of the planet.

The strategic importance and cultural intensity of ‘Gib’ is out of all proportion to its diminutive size – one mile wide by four deep – and its population, about the same as a small British town. And, walking along Main Street, you feel you could be in High Street UK except for the implausibly benign climate and fascinating ‘Strangely strange but oddly normal’ vibe: if Gibraltar had a theme tune, that late 1960s song would surely be it. The title is appropriate for this geopolitical oddity, a chunk of Britain squeezed between Spain and Morocco. Equally apt is the time that this song was released by those no-hit wonders, Dr Strangely Strange. It is commonly said that time in the Crown Territory is calibrated about four decades behind the rest of Europe – indeed, to about the time when John Lennon and Yoko Ono married in Gibraltar on 20 March 1969.

Anyone who has such a misapprehension should step right this way for a magical tour to unravel the mysteries of Gibraltar. The future has arrived in the Rock – and a place once seen as a backwater now offers the coolest city break in southern Europe.

Wheels down? Look just south of the runway (and if you’re not sure which direction that is, Gibraltar provides a big, fat clue in the shape of the Rock). You will see a colony of yachts basking in the sun alongside designer shops (John Galliano, the Dior designer, was born here) and breezy bars: Irish, North African and Champagne. This is Ocean Village, where Gibraltar’s future is already flourishing. The colony has a long history of international investment, not least because of its role in the offshore banking business. Now, though, the cash is pouring in to transform Gibraltar’s image and appeal. This smart new waterfront complex may look as though it has been shipped straight down the coast from Marbella, but this is a uniquely Gibraltarian creation: and you can walk to it from the airport. Formalities at Gibraltar’s diminutive airport are brisk, and anyone arriving from the UK has no need to pause to change money: this is one part of Europe where your pound is still worth £1. If you turn right out of the terminal, Spain is all of – ooh, walking slowly – two minutes away. But turn left and the road leads directly across the middle of the tarmac where you landed five minutes earlier.

Gibraltar has learnt over the centuries that pragmatism pays. By the time you have been here a couple of days you will probably regard crossing an active runway as oddly normal. But the first time you walk towards the heart of Gibraltar, looking left and right for air traffic under the watchful gaze of navy personnel, it feels strangely strange. So, when you reach the far end, does the way that the road entwines with the fortifications that have protected Gibraltar through the centuries, as the colony has gradually grown in prominence and diversity.

For humanity down the ages, the Rock has enjoyed a succession of advantages. Our prehistoric predecessors could shelter in the natural caves of this sandstone slab – indeed, Neanderthal man is a misnomer in terms of scientific history. A skull of one of these ‘nearly men’ was found here in 1848, eight years before a more celebrated version of the same species was discovered in the Neander Valley of western Germany.

Among the waves of occupation in Gibraltar since history began to be written, the Moors were the people who originally made Gibraltar and gave it the name, which is a corruption of the term meaning ‘Tariq’s mountain’. The warriors from present-day Morocco used it as a foothold in the Iberian peninsula for the Islamic sweep across Spain. The most spectacular part of the Moorish legacy is the Tower of Homage that looms powerfully over the skirts of the Rock. Externally it looks almost rudimentary – a square tower rising from the rock. But delve inside this 12th-century structure, and you discover some intricate Islamic decoration as well as one of the finest views in Gibraltar.