Firstly, I have to say I am a great fan of sparrowhawks and to have one in the vicinity is wonderful.
An observation: sparrowhawks often take their prey to the same place to kill and devour it. There was a time when pigeon remains were frequently to be found on exactly the same bit of lawn in our local park and I wondered why and how it was the sparrowhawk managed to catch and kill the pigeon in exactly the same place every time. The pigeon is bigger than a sparrowhawk and it would not be possible for the sparrowhawk to carry a pigeon's corpse (see also swallow* and coconut).
Then one day, when I was walking the dog near Hadleigh Castle, there was a kerfuffle in the hedge and a sparrowhawk landed slap bang on top of a collared dove. What happened next left me gobsmacked. The sparrowhawk, its talons gripping the collared dove's back, then allowed the collared dove to take off, and directed it to where it wanted it to go. I didn't see the conclusion of this particular meeting, but I feel sure it didn't end well for the collared dove. So the sparrowhawk does not carry pigeons after all! It steers them alive to its "killing field" where it then settles down to lunch. How sinister is that?
It would be my guess that your sparrowhawk has selected your lawn as its dining room, but it probably catches its blackbirds in lots of different places and then takes them there. I'm sure its presence would be likely to deter birds from coming into your garden, but I would just look upon it as a privilege to have such a wonderful but deadly creature to admire. As has been mentioned above, if we want sparrowhawks, then we must be prepared for them to do what sparrowhawks do. Drivers of motor vehicles no doubt kill far more local wildlife than sparrowhawks.
*European, since you ask