Cannot remember the date the law changed, but way back when, swan was classed as a 'Wild Fowl' as was duck, goose, coot etc. and could be shot as they.

I believe (but may be wrong) that Peter Scott held the record at one time for the most swans shot during a 'flight'. (Session of wildfowling). He later went on to form what became the RSPB.
If I am wrong I apologise to his memory!