Is it really true that all Swans in UK are property of Queen? What is reason behind it (if any)?
To answer the question of "why?"....
This is the official web site of the British Royal Family. Written and managed by the Royal Household at Buckingham Palace, the site aims to provide an authoritative resource of information about the Monarchy and Royal Family, past and present.
The History of Swan Upping
As early as the twelfth century, the Crown claimed ownership of all mute swans in the country because the birds were highly valued as a delicacy at banquets and feasts. In the fifteenth century The Worshipful Company of Dyers and The Worshipful Company of Vintners were given the right to own swans on the River Thames.
I think that in a feudal society the crown owns everything (the whole country and everything in it), by default, and gives away certain rights -- e.g. "you can have this duchy", they might say to a duke; the duke in turn would subdivide and assign various rights to his vassals.
Amoung these rights was the right to hunt. Medieval hunting:
In Roman law, property included the right to hunt, a concept which continued under the Frankish Merovingian and Carolingian monarchs who considered the entire kingdom to be their property, but who also controlled enormous royal domains as hunting reserves (forests). [...]
With the breakup of the Carolingian Empire, local lords strove to maintain and monopolize the reserves and the taking of big game in forest reserves, and small game in warrens. They were most successful in England after the Norman Conquest, and in Gascony from the 12th century. These large sanctuaries of woodland—the royal forest—where populations of game animals were kept and watched over by gamekeepers. Here the peasantry could not hunt, poaching being subject to severe punishment: the injustice of such "emparked" preserves was a common cause of complaint in populist vernacular literature. The lower classes mostly had to content themselves with snaring birds and smaller game outside of forest reserves and warrens.
By the 16th century, areas of land reserved for breeding and hunting of game were of three kinds, according to their degree of enclosure and being subject to Forest Laws: Forests, large unenclosed areas of wilderness, Chases, which normally belonged to nobles, rather than the crown, and Parks, which were enclosed, and not subject to Forest Laws.
In summary they "belong" to the Queen because the Crown claimed the right to have/hunt them.
Not all swans in the UK are property of the Crown.
From the Wikipedia article on Swan Upping:
"By prerogative right, the British Crown enjoys ownership of all unmarked mute swans in open water. Rights over swans may, however, be granted to a subject by the Crown (accordingly they may also be claimed by prescription.)"
In The Seventh Part of the Reports of Sir Edward Coke, Knt. Lord Chief Justice of the Common Pleas it was established that, "Every one who hath swans within his private waters hath a property in them"
So, Individuals and companies in the UK can own swans and keep them as property. The Crown does not own all wild swans as property. The Crown has the prerogative to capture wild swans and claim them as property of the Crown.