Privacy Bush

If your garden is....Traditional style: Privet; does not mind clay. However the pollen can cause quite bad respiratory problems/allergic reactions and it's a slow grower.
A Native garden: Grevillea Olivacea; It is fast growing but needs some pruning to keep the shape compact. Quite dense foliage. We have one in gravelly clay and it's doing well. You can get red or apricot flowering varieties.
Tropical style garden: Tiger grass; It is a form of bamboo but will grow in heavy soils. Clumps, and can become hard to remove/prune but very effective as a screen. We have some on a boundary fence.

With any plantings, make sure you add a clay breaker like gypsum to the hole to help with drainage. All of these need some shaping so you can prune to the correct width as necessary.

No worries, I just remembered the leptospernum (or tee tree) I have. It's called Lipstick and it has masses of pink flowers in spring. It will tolerate clay and grows no more than about 1.5m high and 1 metre wide, saving you the trouble of pruning except for compact form. It will make a good informal hedge. (I have seen olivaceas growing up to as much as 4 mtrs high in certain conditions).
Perhaps the teatree would be a better alternative for you, and its flowers are very attractive.

A leptospernum (teatree) is what I would suggest; the foliage is much less prickly than grevilleas (in general) and that is an advantage when you might be brushing up against it. My favourite of the teatrees is "Leptospermum petersonii" - the "Lemon Scented Tea Tree", but I believe it would be too wide for your situation!