I had to mount some wall cupboards onto a stud wall and here's what I did. It may be overkill, but I prefer it that way
The wall will be created by vertical battens positioned every 16in or so. You can get a device called a stud finder or drill some holes and use a piece of wire to feel behind the plasterboard until you locate the studs. If you always win on the lottery, offer up the bracket and screw straight into those studs with standard wood screws and the jobs a guddun'.
If you are not so lucky, you can cut the plasterboard vertically down the centre of two studs and across horizontally, so you remove a rectangle of plasterboard. Try to keep it for a template if it comes off in more or less one piece. Then cut a piece of timber to fit in between the vertical studs horizontally where you need your bracket. You can screw either end into the existing battens and/or drill a larger hole half way and then a smaller hole into the actual horizontal batten, then use a masonry anchor to screw it into the breeze block (that assumes the timber is the same thickness as the existing battening. When you are done MARK IT, so you don't lose where it is and either replace the plasterboard with a new piece, with plasterboard nails and skim over to make good.
That is how I would do it, but it involves a bit of work.
Graham