I would say it's more likely down to the weather rather than the food you've been putting out, I think the wet weather we've been having will have affected a lot of birds.
I don't know how your neighbours know it was your food that had killed them, one thing I do know though they broke the law by disturbing an active nest.
I shouldn't worry about it, Pete. I agree with Alan that it's far more like that they died as a result of the weather. We've had a very cold and wet Spring this year with it changing so rapidly.
The good thing is that Blackbirds will often have second or even third broods so don't despair.
Thanks Alan and Teejay,I appreciate your valued information, Kindest Regards Pete