How can I hang my cupboard on a stud wall?
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.