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If you can screw straight into the wooden wall studs then that's ideal. Unlikely, though, so if there's not much of a gap between plasterboard and brick you could go right through and mount in the brick with a rawlplug.
Otherwise I'd just go with a bigger metal cavity wall anchor. After I needed to refix a radiator to a cavity wall, my internet research led me to "Molly Piranha", which needed an 11mm hole. I had to get a new drill bit, but they've held excellently.
Nice one, yeah already done but I'm going to have to become well aquatinted with various types for different jobs. Have some IKEA Svalnas shelves to put up at some point which have verticals fixed at 3 points. Not sure if I should aim to fix right back through the boards and into the brick/block if possible.