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I would like to build three drawers and a cupboard here:

enter image description here

You can just see the dishwasher to the right, so the wide drawer is for plates and the narrower drawers for cutlery and such like.

The back and side walls are of plastered brick, while the counter above is concrete.

The photo is not terribly clear but there is a rather ugly PVC P-trap sticking out of the middle of the sink, with the effect that there is only around 15" clear from the ground to the bottom of the p-trap. Since both the sink waste and p-trap are very generic models, I am sure I could find an extra inch or two of height without too much difficulty.

Anyway, the main question is what ways can I build this structurally?

I think I need a piece of plywood to form the bottom of the cabinet, and then the left side of the cabinet would be another piece joined to that one. However, because of limited space, I'd like to join the plywood bottom to the concrete wall. I'm not sure how best to do this (e.g., with an L-shaped metal bracket)

The wall at the back being brick/plaster is obviously very solid, so I'm not sure if I need to use a full plywood back or if it's sufficient just to use a top and bottom rail at the back and fix that to the wall.

Secondly, I need to support the left side of the two smaller drawers. I suppose a full length rail would be better structurally, but I'm not sure if that's necessary or if I could just join that panel to the back brick wall using two half-width rails, and then join it to the side wall with two more rails which I anchor to the concrete using brackets or whatever as before.

Am I thinking about this wrong?

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    Hi, welcome to Woodworking. I've changed the wording of the title and some in the body of the Question because there's rarely one best way to do anything in woodworking and ranking options for best automatically makes for subjective Answers., Also your "Obviously I need a piece of plywood to form the bottom of the cabinet..." actually isn't a given; I've seen similar units of utility shelving/cabinetry where there isn't a bottom because there doesn't need to be one structurally and by not including it you save time and material.
    – Graphus
    Dec 8, 2021 at 0:23

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I'd just build a small, free standing cabinet that fits into the space. At some point you will need access to the stuff in back, and it will be a lot easier for future you if it is just something you can remove in 1 piece. You might want to consider putting some casters on the bottom so it can be wheeled in and out like a dishwasher.

Cut a sheet of plywood that fits the opening you want to cover, then work backwards from there with the sides and drawers.

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    Yeah, 100% I'd make this a freestanding unit that can just slide out if/when needed. I think it would be bonkers to fix this in place given the location near plumbing (and an electrical outlet?).
    – Graphus
    Dec 8, 2021 at 0:25
  • Yup! Looks like there's some sort of gauge behind "cupboard" and the middle drawer is hiding what looks like an outlet. Besides, attempting to line up the 3 drawer slides and attaching them to the concrete wall on the right will be a ---nightmare--- more difficult than necessary.
    – FreeMan
    Dec 8, 2021 at 0:43
  • Good idea to make it freestanding. I would have built it in place and had to deal with a sink clog three days later....
    – gnicko
    Dec 8, 2021 at 14:57
  • Exactly what I was planning to say.
    – bowlturner
    Dec 8, 2021 at 16:36
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    Additionally, I'd recommend exterior grade and/or pressure treated plywood, at least for the cabinet carcass. Concrete will wick water through it and that water will end up on the outside of your cabinet. You want the thing to last, so plan for it in advance.
    – FreeMan
    Dec 8, 2021 at 17:29

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