Best way to mount a floating L-shaped desk to a brick wall
Reading from other comments here - 1cm round or 1cm square pipe just sticking straight out of the wall on its own will not cut the mustard. You should be thinking of some type of right angle support bracket. With a 60cm side shelf, supported along the wall on a solidly mounted strip, that right angle bracket should come out under the shelf to at least 50cm and have a vertical side against the wall as far down as feasible. I would think that the vertical span of the bracket should be at least 20cm. The length of the third side of the triangular bracket would best be if it was full length but if the vertical and horizontal sides of the bracket were really sturdy then the angled side could be shorter. 



Brackets like this could be purchased ready made or fabricated out of wood or metal. 

Note that with brackets like this a good share of downward applied force at the outer edge of the shelf will get translated to pull out force on the mounting strip and the upper fasteners on the bracket edge against the wall. You will have to make sure to use fasteners into the brick that can withstand this pullout force with a good margin of safety to ensure that the shelf is secure. You should definitely be thinking in terms of someone coming along and trying to sit on the edge of the desk even is that is never the intention.