plastic sheeting will not work, it needs to breath,
for a veg patch if you can raise the level by creating a bed it will work far better, and makes for much easier effort free gardening,
I obsessively make compost, compost is the key to it all, stop everyone walking where you want to plant/improve, use scaffolding planks to work from, compacting the ground really doesn't help,
mark out your bed (never wider than you can reach the middle from leaning in from the size),
if you put in sides(wood) once you have dug it over once, that is the last digging you will ever have to do, dig over,
add all the leaf mulch(your children should be making bags of this for you every autumn, fill black bin liners with leaves, leave behind shed, for a few years, by year three, you will have a continuos supply which you just dump on the beds.
and or well rotted compost you have, and or well rotted manure.(very cheap from anywhere with horses,
bung in a couple of handfuls of worms, children are good at being sent out to collect them, or order from
if you put a breathable membrane on top and weigh down with stones, so no light gets in, leave for a couple of months
Clay is the brilliant, but only if you get fibrous things into it to break it down,
I have three compost piles(small garden but I divided it into three), made out of hardwood pallets, turn them over often,
I make my compost (treat the process like cooking a favourite recipe), layer of household left overs(no meat), add a handful of compost worms(from yours or a friend's wormery), get your worms going once you have a huge amount everything speeds up,
layer of garden rubbish/weeds,
layer of ripped cardboard/newspaper/twigs.
repeat,
add comfrey(grow this anywhere you have a gap, also use as a mulch as slugs hate it,) often.
repeat, thin layers until it reaches the top,
keep covered with non foam backed,carpet( works as a membrane) and helps to keep the compost warm,
leave and check often, if the grass snakes/slowworms move in you are getting it right, no cooked food (that goes in your wormery the only things that can't go in a wormery is citrus and onions)
when it has got going, turn into the compost area, just rotate occasionally, it ready when it is uniformed, and crumbles nicely, keep moist, but not too wet,
On some of my beds I keep membrane down and use a blow torch to make holes in lines plant plugs into hole, no weeds, less watering, effortless gardening really,
I have used the clay from my garden to make outside ovens, so i do understand how hard it is to see a how you can garden it,
Get into compost, get into worm rearing, and get some raised beds for fruit and veg,
I also add well rotted manure and clay from the garden broken up to my compost factory, if the compost looks too wet, add cardboard, twigs, old straw, if looks too dry add food waste, and foliage.
the best vegetables, fruit and roses are grown in clay rich soil, so if you have clay, in someways you have a head start.
the extra minerals will really pay off, you just have to get the compost in there.
If you have lawns, use a fork ram it in, fine sand into two holes, fine compost into two, repeat, repeat, repeat, do a few with no fillings,
if you do this you will start to see major improvements, as the worms move and mix under the grass, drainage will improve, children are very good at filling the holes.