More DIY advice sought

In masonery, is there anything you can do if the hole is too big for the rawlplug? I tried using a bigger rawlplug but then I find the screw is too small to make it expand properly, and I can't use a bigger screw because it won't fit through the hole in the bracket we're using for these blinds. I have this idea that if only it would stay put and not spin or push in then everything would be fine, which leads me to imagine things like dipping it in Polyfilla before shoving it in the wall, but that's probably not wise in real life. Any ideas?

Thanks!