I have also found that the blur tool does not work. I have tried changing the settings for the brush--one poster suggested moving the "hardness" and "flow" sliders back and forth to get Affinity Photo "unstuck"--and toggling the lock next to the "(pixel)" line for the layer. However, even though the layer is set to pixel, I still can't get the blur tool to work no matter what. I've had to just use the rectangular selection tool and then blur the selection with a filter, but this is kludgy and not what I paid for this software to do.
I am running Affinity Photo 1.7.3 on a Mac running Mojave. I recall that older versions of Affinity Photo seemed to have a blur tool that worked for me.