The king of the siren imitators is the Starling– they mimic all sorts of bird calls and man-made sounds including speech. I remember one in Ullapool that imitated the sound indicating that Stornoway ferry doors were closing so well that we thought we’d missed our crossing.
The song of the Blackbird is much more mellow and melodic and I’ve never heard them mimic but I believe that they can.
As one of the purposes of bird song is to hold and maintain territory, perhaps increasing its repertoire by copying this jarring element from its environment gives it some ‘edge’ as it competes for space and mates.
It’s also possible that this call has been passed down through the Blackbird generations!