So why a reflex recurve not the traditional English Longbow? Well mainly beacuse personally I believe the Cornish Celts used recurves not the traditional English Saxon longbow of the rest of conquered England. My reasoning for this? Comes from the origins of Britian and the Trojans arrival in Cornwall in around 1250BC with reflex bows.

Perhaps the most common cultural characteristic of the ancient Celts was the Celtic languages, a branch of the Indo-European family of languages. The earliest established origins of Celts dates from c.1000-800 BC in Eastern Europe, though research and excavations in very recent years indicate that cultures in Siberia and Northern Mongolia may well be directly linked to the Celts. Both of these cultures date back as far as the second millennium BC. The prowess of the Celts as master horsemen with the capabilities of travelling very long distances give these links further credibility.

These bows are mentioned in Book 21 of Homer's Odyssey. The contest with Odysseus' Bow: Described:

His well-sprung bow was there,

and quivers, too, with lots of painful arrows,

gifts he had received from Iphitus, his friend,

son of Eurytus, a man like the immortals,

when they'd met in Lacedaemon, in Messene,

at the home of wise Ortilochus.

There is the a competition to string the bow, which proves impossible - however it's solved by stringing the bow while seated - which is the case for a Reflex recurve - thus this well sprung bow used by Trojans is the reflex.

But where the Cornish connection? Well:

http://www.gandolf.com/cornwall/giants/gogmagog.shtml

Geoffrey of Monmouth in his Historia regum Britanniae (1135–39), says the founder of Kernow was a Trojan warrior who accompanied Brutus the Trojan, the legendary founder of Britain, to England. on the founding of Britain - The bit particularly about Cornwall. In which Corineus is mentioned as coming from the Trojans and thus reflex bows.

The Prophecy of Diana

Brutus took the Augur Gero and twelve elders and set out for the temple. When they reached the statue they set up three hearths and poured a libation at each. Brutus himself stood before the altar of the goddess with a vessel in his right hand filled with wine and blood from a white hind, in accordance with an ancient ritual, and turned his face upwards to the statue, and said nine times:

O powerful goddess,

Terror of the forest glades,

Yet hope of the wild woodlands,

You who have the power to go in orbit through the airy heavens

and the halls of hell,

Pronounce a judgment which contains concerns the earth.

Tell me which lands you wish us to inhabit.

Tell me of a safe dwelling-place where I am to worship you down the ages,

And where, to the chanting of maidens,

I shall dedicate temples to you.

Brutus then went around the altar four times, pouring wine upon the sacrificial hearth. Then he lay down on the skin of a hind stretched before the altar, and at length, fell asleep.

At about the third hour of the night, the goddess stood before Brutus in a vision, saying:

Brutus,

Beyond the setting sun,

Past the realms of Gaul,

There lies an island in the sea,

Once occupied by giants.

Now it is empty and ready for your folk.

Down the years this will prove to be an abode suited to you and your folk;

And for your descendants it will be a second Troy.

A race of Kings will be born there from your stock

And the round circle of the whole earth will be subject to them.

Arrival in Albion

Brutus and his fleet sailed with their ships full of riches and came ashore at Totnes. At this time the island of Britain was called Albion and uninhabited except for a few giants. It was most attractive because of its great forests of game and rivers which teemed of fish. Brutus and his companions were filled with a great desire to live there. They explored different districts and drove the giants they found living in caves into the mountains. Brutus divided the land amongst them and they began to build houses and cultivate the land so that, in short time, one would think that the land had always been inhabited.

Naming of Britain

Brutus called the island Britain from his own name and his companions he called Britons. He intended that his memory be perpetuated by the derivation of this name. A little later, their language which had been known as Trojan or Crooked Greek was also called British.

Naming of Cornwall

Corineus, following the example of Brutus, called the kingdom that had fallen to his share Cornwall, after his own name, and the people who lived there Cornishmen. Although he might have chosen his own estates before all others who had come there, he preferred the region now called Cornwall, either for its being the cornu or horn of Britain, or through a corruption of his own name.

http://www.thebookofdays.com/months/nov/9.htm

The statue of Corineus at London beidge erected in the 1500s showing him with a reflex Recurve and arrows upon his back.

In 1554, when Philip and Mary made their public entry into London, 'two images, representing two giants, the one named Corineus and the other Gogmagog, holding between them certain Latin verses,' were exhibited on London Bridge. When Elizabeth passed through the city, January 12th, 1558—the day before her coronation—' the final exhibition was at Temple Bar, which was "finely dressed" with the two giants, who held between them a poetic recapitulation of the pageantry exhibited.'

There's also of course the other Celt and Pictish reces of Britain to consider the Irish were unfamiliar with Longbows and so too the Scottish. However the Welsh - were the origin of the longbow which pretty much overtook all other forms of bow in England in the 13th Century had not only longbows but recurved horsebows, I've yet to find much on them but the image of this American replica looks pretty similar:

During the Anglo-Norman invasions of Wales, Welsh bowmen took a heavy toll on the invaders. The English were quick to realise the impact that the longbow could produce on the battlefield. As soon as the Welsh campaign was successfully over, Welsh conscripts began to be incorporated into the English army. The lessons the English learned in Wales were later used with deadly effect by Welsh mercenaries on the battlefields of France and Scotland. Their skill was exercised under King Edward I of England (r. 1272–1307), who banned all sports but archery on Sundays, to make sure Englishmen practised with the longbow. As a result, the English during this period as a whole became very effective with the longbow.

But were these bows the traditional tool of the ancient archer? They are cruder and less technical to make than the ancient reflex and I feel it was this ease of construction which led to it being the weapon in the UK. But if we had Trojans in Cornwall then we'd have had their bow technology and perhaps the Cornish bow was once a recurve. Especially if we were a nation of mounted militia - celtic horse skills are well documented and a long bow would be irrelevent on horseback or celt chariot.

Infact the BBC gave Robin a reflex recurve in the last TV adaptation explainuing it by saying: The bow Robin carries is not a typical English bow (longbows did not arrive until just before the Hundred Years War); it is a recurved bow, supposedly adopted from the Saracens he fought on Crusade. In reality it is an Hungarian hunting bow - the glues used in Saracen bows would have meant it would quickly fall apart under European weather conditions.

Any archaelogists studying in Kernow may be able to she some light on if any recurve remnants have ever been found.