Need to improve dense clay soil – mulch first or add topsoil first?

Hi, I could do with some advice about my awful clay soil please?
The front garden of my new house is basically one large, terraced border full of clay soil. The only things planted there when I moved in were a few rose bushes and hydrangeas dotted about. I'm slowly adding more plants but I want to improve the soil which is either rock hard and cracking in hot weather, or collects standing puddles of water when it rains.
At least there are plenty of earthworms, so I’ve started to dig and incorporated some rotted manure and compost. I want to continue to improve the soil, starting by mulching with a lot more manure and compost over winter.
However, I also have access to several hundred litres of good topsoil from my back garden behind the garage, which the previous owners had used as a dumping ground for clippings. After clearing the clippings, underneath was piles of lovely soil. I need to reduce the height of the pile to protect the garage from damp. The logical thing would seem to be to spread it on the clay wasteland in the front garden!
My question is, if I add topsoil first before laying down
the mulch, would this prevent the worms from dragging the organic matter down
into the clay and improving it? Is it better to just lay the manure mulch over
winter and add the topsoil in spring?

Posts
I'm not sure that's what it is - it's more likely to be compost if the previous owners were putting other material on top of it. If so, that's a highly beneficial soil conditioner anyway, so it would be ideal as a mulch after planting
I live in west central Scotland - not where that photo is...
Over the 34 years I've lived here I've been regularly adding organic matter to improve the friability of the soil and it works.
Topsoil by itself will have little impact - you need lots of organic matter to break up the clay, but if you have it, use it.
Mushroom compost is good as it contains lots of straw, but can be quite alkaline.
Horse manure/farmyard manure is also good, but these days it tends to have a lot of wood shavings in it which, if not dug in, tend to blow around all over the place in the winter winds.
Home made compost is excellent - my compost bins produce about 1 cu m per year.
Clay soil is actually full of good stuff, but it's too tightly bound. Adding lots of organic matter frees it all up.
If you have the chance to dig it in a bit that's great, if not, let the worms earn their keep.
Billericay - Essex
Knowledge is knowing that a tomato is a fruit.
Wisdom is not putting it in a fruit salad.
Manure with a lot of shavings just shows the people doing the mucking out aren't very competent
I live in west central Scotland - not where that photo is...