Sorry this is a long answer and probably not you want to hear.I hope somebody else can be more helpful.

Am wondering why you are watering them as you say they are far too wet already? Overwatering can cause as much damage as underwatering and few things will grow happily in watgerlogged soil..
Any material to improve the soil needs digging in throughthe topsoil layer so that it is evenly distributed and its a good plant to fork well into the heavy subsoil too to break it up a bit. But even then shingle won't do much for the soil structure, and as the tree roots go down deeply putting shingle near the surface won't make any difference to the drainage.. Ideally a smaller grit would have been better than shingle as the aim is to improve the soil structure as well as improve drainage but it still needs incorporating with the soil. If you want shingle to improve drainage it needs to be much deeper. If you just dig a deep hole and fill it with shingle the water will flow into the hole rather than drain away.
Clay in a garden isn't all bad news as it can be pretty fertile but it does need improving with something to make it lighter - well rotted compost is a good choice.

But as the other three trees are OK this may not be the problem at all. Transplanting mature shrubs and trees is difficult and its often better to start small, so you have done well with the others If the tree dies but the sucker still looks good you can cut the trunk off above it and grow it on.

Bear in mind that there is a height limit for hedges between neighbours. Sorry after all this I don't seem to have been much help...

Thank you very much for your comments. Much appreciated.

Do you think I will lose the tree?

Should I prune the tree?

When I dug the drainage holes next to the root ball, these holes where made much deeper than the root ball itself. I noticed at the time, water ran from the root ball itself into these holes. Before I created the drainage holes I hadn't watered the trees for about 13 days. Only now do I water the trees with a very small amount of water and food due to hot weather so that the root ball doesn't dry out.

Unfortunately the landscape company that I purchased these trees from and who also dug them for me didn't check/prepare the soil.

As said by Steragram, when the trees were planted they should have mixed the top soil with coarse grit. Digging drainage holes nearby with only encourage more water into the vicinity. I wouldn't feed them or use too much water for a while and see what happens. I'm sorry to say though, that Photinia, in my opinion isn't the most suitable tree to plant in heavy, waterlogged soil as it does best in a moist but free-draining soil. I know that you were looking for evergreen trees for the privacy but something like Prunus laurocerasus cherry laurel or Hawthorn (Crataegus monogyna) would have coped with the conditions better. If any of the trees do fail, then I would be inclined to call back the landscaping company who supplied and planted the trees as I know they were very expensive trees.

Will the tree die? -looks likely.
Should you prune it? No, this wouldn't help.
Feeding any any of them shouldn't be necessary.
Watering: A good watering less often is much better than a little more regularly. This is because roots will go in search of water and a small amount of water only wets the top few inches and encourages the roots to grow near the surface where they are then in more danger in dry weather. A gallon once a week is better than a litre every day. But if the ground is really wet then watering shouldn't be necessary at all. Stick a trowel into the soil (well away from the trunk!)and see what the soil's like well below the surface.

If and when that tree dies planting a Portuguese laurel (aka cherry laurel as Jimmy suggests)and growing as a clipped shrub might serve. You can keep it fairly small or let it grow quite tall, but clipping at least once a year would be needed to prevent it getting sprawly and leggy - unclipped they can be very untidy and very open and wide. Clipped they they can be a neat rounded bush though you would have to curb your impatience and not let it grow tall too quickly or it would develop a lot of bare branches with greenery on the ends..Come to think of it I have seen them growing in a neglected really boggy place but they were extremely lax and untidy.. The leaves are a similar shape to the trees you have already but stay green. But you wouldn't be able to buy a tall clipped one ready grown. Anyway its better to start small- things establish better.

But as Jimmy says go back to the supplier. Trees that size may well come with some sort of guarantee, especially if the company did the planting for you.