attaching floating shelves to solid wall with anchor screws
The anchor screws you show are simply too short for that type of shelf. They seem to be designed for anchoring lightweight objects to plasterboard. They are not suitable for plastered brick walls or for shelving that may carry heavy loads like books or heavy ornaments.




I would go out and buy some long screws (say 5cm) and conventional wall-plugs. You will need to drill-out the holes to a wider diameter to suit the wall plugs you buy.

You will probably need to buy a normal length masonry drill bit (probably 7 or 8 mm diameter depending on wall-plug) 



Use it in a drill that has a hammer action (a combi-drill will do - borrow one if you don't own one)

If you need to buy a combi-drill - you'll find that wired drills are cheaper and more powerful - much better for drilling into brick.

If money is an issue, buy one from a local Wilco, it will likely last long enough to get this job done :-). B&amp;Q sometimes do a special offer on the halfway-decent Bosch PSB680RE