Let the pigeons out, spray inside nicely with insecticide, let it stay for 15 minutes and wash everything with water and bleach.
You need to treat birds too (I use Ivermectin - one drop on the back of the pigeon)
The mosquito spray that you mentioned probably won't kill the bugs in the loft. They are made to REPELL mosquitoes, not kill them. And the smell could be too much for the birds. They have very delicate respiratory systems. Can you get a bird spray, for caged birds? You could spray the loft and the birds with it. Or Garden dust with permethrin in it? You could put it around the loft, leave it for a bit, then clean it out before returning the birds. It can also be put on the birds.