Some observations from a retired Joiner.
If you'd fitted the wooden packers vertically, you'd have a much better chance of a decent fix. You could still do this of course, just a bit of a bind. Personally I'd have cut them to suit, then trimmed so they sit totally plumb with the wall, but a miilimetre or so behind the actual face of the wall. Then brush down the brickwork where the packers are to go, so the area you're fixing to is totally clean. If you can't get a decent fix with a plug and screw, get some decent construction adhesive, Gripfill or similar, then apply a nice thick bead or two to the packer, push firmly onto the wall, then pull back off. If there's Gripfill on both the wall and the packer, you're good to go and simply push back on.
What size and style skirting are you fitting? I'll assume it will cover the plaster line in the pics, so run a scraper around the plaster line to remove the small 'kick' that plasterers always leave behind.
Butt and scribe internal corners, never mitre internally! The skirting will linevitably shrink a small amount, and a mitre will open up. Mitre external corners, which goes without saying.
Which leads to the next point, if the skirting is getting painted, make sure you paint the BACK of the skirting with some decent undercoat, that will stop it cupping/curling when it's been fitted back to the wall a couple of days, same if you're staining/varnishing. In fact either way you could paint/stain all faces and edges just to be safe.
When the whole room has been cut and fitted to length, mark off the skirting where the packers are fitted to the walls, then apply some more Gripfill, push on/pull off as before, then reattach.
If the skirting tries to pull away from the wall, either because it's a tight fit or due to it being a liitle bowed, you'll need to find a way to brace it in place until the Gripfill takes hold. Just nail an offcut to the floor (aware it's a new floor, couple of nail holes are easily filled) then brace from there to the skirting with whatevers around so that the skirt is under tension.
If you want to use screws instead, feel free to do so, but then you have the task of filling and sanding, or if stained plug and pelleting the screwholes.
Hope this is of some use, any questions feel free to ask!