This desk is the simplest and cheapest design I could come up with. The design is based on half joints as they provide an easy and strong assembly. All the parts are slotted together.
The 17mm plywood "X" legs can be modified and upgraded as you want. Here they are 730mm high. For the top I used 16mm chipboard, which is 2400mm long and 600mm wide.The span between the supports is 1700mm. I got my wood for 10 pounds from a timber recycling centre but it can be easily picked up for free.

No screws, no worries :)

Tools:
Jigsaw or Hand Saw to cut the pieces
Jigsaw or Drill to make the holes in the plot surface
Better Jigsaw :)

Step 1: Cut Shapes and Holes

Cut the supports in desired shape and position them on the top surface for precision :) Then cut the top part so the feature can go trough the "X" shaped hole in the plot. Here the distance between the back and the parallel plane is 200mm. Also I suppose the "X" shaped support can be rotated diagonally and shelves can be added...

Cut the plot surface "X" holes using drill to make few holes and then shape them with the jigsaw. It's possible to entirely make the holes with the drill and then a rough file.