I wouldn't bother with manure at all at this point. Digging things into heavy clay is a waste of time and effort. You're in the UK, I'm guessing you're on an allotment? My preferred method of alleviating clay soil is to plant half in a cover crop and the other half as my "garden. Buckwheat is a good cover crop, I once got 3 crops in a single season in OH, not sure what your growing conditions would allow. I liked the buckwheat because it would set seed and I could just mow it over or weed whack it down after it set seed, leaving the stems where they fell, and it would self-sow another crop. Then the next year I would switch sides. It takes some time but so does double digging. Or digging at all.
Second option if you don't have the room, time or energy for plan A, is to lay down cardboard. If you have lawn clippings or other compostable material lay those down first then cover with the cardboard. Then cover the cardboard with whatever type of mulch you have at hand. I used to use spent straw or hay (understanding this can bring in CONSIDERABLE quantities of weed seeds which doesn't matter if you layer it deeply enough, but does if you are putting down thin layers), now I use wood mulch (undyed, that's a thing in the US, hope its not a thing in the UK).
Just plant your plants through the cardboard. I wet the cardboard before laying it, also the ground should be moist but not waterlogged. Then immediately cover with mulch. I use drip irrigation, either the drip hose or the solid hose with emitters space where the plants will be. It can go under the cardboard or between the cardboard and the mulch. In dry areas, under the cardboard. In more humid areas I've never had a problem just putting it under the mulch, and 100% just under the mulch if you're using emitters and not soaker or drip hose.
The only issue I ever had was in a very humid area where there were sluggs. I say sluggs to convey the ugg factor there. See how I did that. LOL! Anyway that's the only time I had issues doing his in 30+ years. That's what slug bait is for.
I use plain brown cardboard boxes broken down (like from amazon). I use to spread them out one layer thick but now I just open the tops and bottoms and put them down 2 layers thick. Less work for me, they last longer in the garden. I've seen single layer cardboard disappear in one season in the past. Worms abounding. The cardboard is more for weed barrier, and will need to be replaced every year or two, the mulch on top probably does more to make the area habitable for my wormy friends. I mean friend that ARE worms, not friends that HAVE worms. Anyway.
I have also used shredded paper but if you do that, be sure to cover it with something dark. I couldn't figure out why my garden wasn't thriving and pulled back the shredded paper I had mulched with and the ground was COLD. It was reflecting the sun and cooling the soil too much - which could be a good thing in certain circumstances but usually is not.
Whichever method you use the worms will come and dig your garden for you. The last time I had to garden in heavy clay soil (new construction that had been backfilled with 3 different kinds of clay, I dug through layers of grey, yellow, and red clay and never hit dirt) I did the whole double-digging-work-organic-matter-into-the-soil thing. The next year, I did it again - only to find the stuff that I had dug in the year before nearly perfectly preserved, like those folks unfortunate enough to have died in a peat bog. So I went to cover cropping, and then to the cardboard with mulch on top. It never takes more than 3 years to end up with lovely friable nutrient rich soil instead of something that gladdens a potter's heart.
The worms are happy. My plants are happy. I am happy. Even my son is happy because now that I am old and decrepit he doesn't have to double-dig my garden for me, LOL!
