You'll need other measures, you can either have a dpm in the concrete and a drained cavity in the wall, or a damp proof membrane all the way. There are other ways that you can research too. I think the approved documents have some examples of how to tank below ground too.
Looking at the height, bear in mind your wall will be retaining the ground behind so it will need enough strength to Gould back the ground and water pressure in wet weather. So you would need enough piers of suitable width or other measures if the wall isn't thick enough.
You don't need to tank because the dpm is holding back the water. So the blockwork will be dry and not subject to frost in general either.
Not sure about where to build, with a 6 inch slab I'm guessing start half the thickness of the wall away would be plenty. But watch out for rain running down the exposed side of the building onto the top of the slab and soaking the inside. You'll need to make sure the membrane doesn't collect any water which would traditionally be by lapping it over the dpc. Not sure the alternative when the dpc is inside the edge of the slab.
My suggestion is to have a separate retaining wall with either ground anchors ( red ) or buttresses ( grey ) .
Clay will swell and shrink depending on how much water is in the ground and swelling clay could exert enough pressure on the wall to distort or break it. Leave enough space between retaining wall and shed wall to allow access to repair the wall(s) when necessary.
Drainage pipes in the clay will reduce the amount of swelling.
I think a retaining wall might be going too far - the cut-in is only 5ft - although I'm wondering about 6" hollow blocks for the rear (the side cut into the slope), just to be sure. Plain blocks for the other 3 sides. (What sort, demnsity of blocks?).
Will the hollow blocks fill with water/damp? Maybe I should use blue brick up to ground level, regular brick above?
Obviously, I want to keep costs down, but damp is my greatest concern.
If you want it to be dry and trouble free build the retaining wall separate to the building.
If you want to incorporate the retaining wall and building, you'll want a good tanking system, a dpm on its own might fail due to poor installation, on the outside with sufficient drainage and infill to stop movement. Remember you'll have the weight of the water on the wall too so the wall will need to be reinforced.
If the length before returns is not too great you'll have sufficient toppling force though I'd still tie the wall into your foundations or you may find the wall is pushed off.
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