I used to run my brother's farm which is in a nitrate sensitive zone. I was petrified whenever I got letters from them!
For farms, the amount of fertiliser applied will be reflected in the run-off and the proximity of streams and rivers will affect how badly the environment is impacted. The amount of humus in the soil will be reflected in run-off too, where seriously depleted soils will have a lot more run off than healthy, humus rich soils.
For vegetable growing, I suggest you don't overdo the application of manures and feeds which are very rich in nitrogen. In fact that's part of organic growing, you just apply what is needed, no overdosing, and you apply it to the soil where you will be growing those plants that need it when they need it. That sounds as if I'm meaning liquid feeds but I mean feeding the soil. You will know which groups of plants need nitrogen, such as brassicas, which need potassium such as tomatoes and so on. So by careful crop rotation and mulching with appropriate manures, green manures, garden compost, then by giving manure tea, comfrey tea, nettle tea or whatever is needed as an occasional boost, you should be able to match feeding to take-up and keep leaching to a minimum. Green manures over winter are important for the prevention of leaching and if you don't use them now they are well worth investigating.
So don't go OTT with the depth of the manure in your initial no-dig areas but match it to the crops you intend to grow there.
Another point I heard of a few years ago, when the government was introducing rules on drainage from muck heaps, is that the problem is mainly for heaps on concrete where there is visible runoff. Gardeners were up in arms, but it doesn't seem to be a problem with domestic garden compost heaps on soil.