Electrical – How to install an electrical panel when the stud cavity is too narrow

While having all four mount points connect to structure (aka: the stud) is ideal, I think in your case, having two mount points in wood and two in a drywall anchor, you're going to be ok.

Consider this question: What is the weight capacity of a drywall screw?

One drywall screw CAN (not should) hold a lot of weight for its size. Also a properly installed drywall anchor can typically stand 70~ pounds of pull force (as in pulling out, not down).

With two WOOD (not drywall - wood) screws set into the available stud and 2 (or better, 4) drywall anchors, I think you're not likely to exceed the capacity. If your cabinet total weight when full is < 100 lbs you're probably not going to have a problem.

You must not support shelving with plasterboard anchors except when there are no other options. Plasterboard just is not that strong. It's important to locate the studs and attach the shelf supports with wood screws through the plasterboard and into the studs directly.

There are stud locators available for minimal expense, but they are not fool proof. One type works by locating the fasteners in the studs by magnetism. Since fasteners only occur intermittently, this is not the best method IMO. Another works by relative density, but is easily fooled by other masses in the wall and is confused by nearby metal. With all your power equipment, this type will not work well unless there is a section you can test that is free of confusing artefacts, such as near the floor level. You can typically assume the studs are reasonably vertical for their full length.

For determining adequate screw length into studs, I'm not sure of common UK construction practise, but you could assume most plasterworks to be from 1/2" to 1" thick. It's less critical for wood screws than plaster anchors to get the exact depth correct. For wood screws, ensure they penetrate into the stud at least 7 shank diameters depth.