Turf, branches, soil and old fencing — sized correctly so you're not paying for two skips.
Midi to builder's skip (4–6 yd³)
Garden waste like soil and turf is dense. A skip that looks half full can already be near its weight limit — if you're clearing a lot of soil specifically, ask about a dedicated soil skip.
Some suppliers separate pure green waste (grass, hedge trimmings, leaves) from general garden waste including old fencing or slabs, sometimes at a different rate — worth asking when you book.
A full garden redesign involving old paving, decking removal or a large hedge clearance usually needs a large skip (8 yd³) rather than a midi.