Ownership of all unmarked Mute swans in open water in the UK has been the monarch's since medieval times when the crown claimed that right. This is asserted by the swan-upping ceremony that takes place in July.
All wild swans in the UK are protected birds including the Bewicks, Whooper and Mute, however, captive bred Whoopers can be sold.
A large swan will weigh about 4kg when prepared for the table and only yield about 2kg of meat. The meat is generally a little tough and has a gamy goose flavour.
So, yes, for the curious it is possible to buy, and eat, swan in the UK but will probably be a disappointment.