(NB when I say ‘manure’ here I mean stacked/composted animal waste which includes some bedding)
Welcome Daffs and thanks for the book compliment and for asking this question, highly relevant to other aspiring no dig growers. But are you using the manure to mulch and kill existing growth by excluding light? If so you need 10cm approx, or a sheet of black polythene on top of 5cm manure (or both!).
I assume your site is mostly grass and grass weeds, including perennials such as buttercup, thistle, nettle etc. If starting with long vegetation it is worth mowing as short as possible before mulching, leaving all the mowings on top.
Prices of manure are nearly all transport so I hope you can find a stables or a cow farm nearby. But the question of aminopyralid weedkiller hangs over all manure now; although only small areas of grass are sprayed, to kill nettles, docks and thistles, it is a horrible poison. I suggest you fetch some from the manure heap and sow peas, tomatoes and salad in it to see if growth is healthy, before taking delivery. Or ask the farmer if he has used it, when buying from a dairy or beef farm – whereas horse stables often do not know how their purchased hay was grown.
Around £10/ton is a fair price but the cost will increase if transporting more than a few miles. I reckon that a 5-7cm layer will need between 75 and 90 tons of manure per acre as this first dressing, in the work of creating a richer, less weedy surface soil. This tonnage sounds a lot until you consider how it is the annual output of about four dairy cows!
I hesitate to give a precise figure because measurements of manure are fraught with variables: measuring the thickness of spreading is almost impossible because of lumpiness, and less rotted manure needs more tonnage because of how it condenses, both to less weight and less volume.
If manure has been stacked for at least 6 months since leaving an animal’s bottom, preferably a year, you can spread it straightaway. If bedding is still clearly visible eg yellow straw and unrotted paper etc, it needs composting (stacked in a heap) for 6 months or so. This helps to lock in nutrients, making them insoluble in water and yet always available to growing plants, i.e they are little leached by winter rain when locked up in cold soil. In my opinion the official guidelines on nutrient leaching from manure do not consider this sufficiently – someone may say you are causing pollution of groundwater, but I say not if the manure has been stacked and thus composted. I can grow wonderful garlic in soil manured in October at planting time, AND brassicas the following summer and autumn in the same soil, which I feel would be impossible if winter leaching were happening.
In your second year, expect to use less than half the amount and also you will have some of your own compost by then, from crop residues etc. Your soil will be growing less weeds and wonderful vegetables.