Frankly, any plant worth its salt will try to get away from a Leylandii. Even if you think the centre of the garden is less sunny, the ambient light levels there must be higher than towards the back. I'm wondering how much distance there is between the trunk of the cherry trees and the trunks of the leylandii or any hedge/fence/wall/shrubs directly behind them? And also what variety of cherry they are?

Bamboo - there is about 3-4 feet between the trunks of the cherry tree and the leylandii. The leylandii are planted hard up against a retaining wall (to ground level (the street drops away a couple of feet outside our garden) and then on top a 6 foot wooden slatted fence) about a foot further away.

The leylandii are there for no other reason than to provide a screen from the busy road.

The trees are only about 4 or 5 years old. It's possible that the cherry tree roots have already extended to the wall but the cherry tree on the other side of the garden which doesn't have any walls (only more leylandii) to compete with is doing the exact same but in reverse i.e. towards the centre of the garden from the other direction.

I can't recall what variety of cherry they are - the one in the photograph may well simply be a wild cherry while the other one (not photographed) is quite ornamental and starting to cover in pretty pink blossom just now.

Bamboo - it's also the fact that they've completely turned perpendicular not a gradual veer towards sunlight.

3 - 4 feet is way too close, so I'm not surprised the trees are turning themselves away. There is no disorder, disease or infestation which may make your trees turn in this way - when plants do this, it's usually because there's much less light behind than in front - it's a clear message from the plant! The only other possibility is that, because the branches are now above the height of the fence, which acts like a breakwind, the wind from that direction is a prevailing one, causing the trees to grow in this way, but as its happening in reverse on the other side, that explanation doesn't really fit the bill. I take it that you intended the leylandii to be kept at a certain height (6-8 feet? More?) which is a costly job every year or other year. For one thing, when the leylandii thickens up, it will probably be 5 feet deep from front to back, which means it will encroach, be in contact with, the trunks of your cherry tree. The gap between them needs to be 10- 15 feet really, as a minimum.
My advice is to remove the leylandii and decide on a different screening method, since it will be difficult to move the cherry trees if they've been in longer than 2 years, and you may not have the room to give them and the leylandii enough space. If you wanted a narrow hedge there, choosing a columnar, narrow plant would be best - bamboo (with a root rhizome barrier) such as Phyllostachys, or a deciduous hedge of something like Berberis Red Pillar, though that may not be tall enough for your needs at 5.5 feet.

Could it be the type of street lighting drawing them. I am only guessing, no ideas other than light drawing them in some way.

Thanks Bamboo - you're not the first GoY-er to warn us about leylandii and you won't be the last I'm sure!

Yes, the plan is to not let them get away from us so 6-8 foot as a VERY maximum - so far we've managed to keep them to an easy 2 foot spread by encouraging lateral growth along the fence and not out into the garden.

The great thing we have found about them to our advantage is that they sook the wetness out of the soil (which I agree would normally be a bad thing, but our garden often get's so waterlogged due to the slope we're on).

They've started to form a great screen from the road and also our unruly neighbour's son next door...for the price of a pair of strong shears and shoulder muscles they're worth the hard work!!

The birds also love the cover they bring which for a new build estate is great news for them.

But the price is the unfortunate effect on your cherry trees because they are too close...

And as Bamboo says they do get wider and wider as they age, not being allowed to grow upwards as they want to.. They do this in spite of being clipped close every year, so if you want to keep both them and the tree it looks as though you are stuck with the problem for the time being.. However as you trees get higher they will be above the shade of the hedge and may then begin to grow straighter.
From the photo it appears that your conifers are planted very near to the fence, so there is the added possibility that as they grow they will be very thin through lack of light or try to thicken up and push the fence over. Next time you want cheering up just send me a message, sorry!

Steragram - haha, that's ok. We will see how it goes with the leylandii...I daren't mention the russion vine (oops) that we have in the garden too.

Without meaning to sound bold or stupid we'll make sure we keep on top of the leylandii (and the russian vine) and not let them become a pest - if they do we'll chop them to the ground.

At the moment their benefits outweigh any negative aspects.

We're not that fussed about the cherry trees - it was more to question the weird phenomenon with them completely changing direction of growth...with cause confirmed we'll see how things turn out.

Be ready for some updates in months / years to come if we start to have trouble with the hedge...we'll continue to stick photos on GoY to keep everyone updated!

Russian vine as well!! Well, you won't be having problems wondering how to fill up your bars spaces at any event,lol.
A clematis montana would grow fast and big (but not quite as fast and big) and have pretty flowers on in early summer, if you ever get fed up with the RV. :))
Hope you have lovely flowers and some fruit on your trees anyway.

If I was planted next to leylandii, I would try and walk away from them too! This tree is the only true plant I hate with a vengeance - detest - they sould be banned. A nice hedge of berberis or any other thorny hedge would fill the gap, make a good screen and deter boysterous kids. Everyone I know who has had one in the next door garden has suffered from it, either with the shade it casts, or the dry conditions underneath it where not much else will grow. I have now vented my spleen and don't wish to upset anyone.

I think leylandii can be useful - in the right place, which, frankly, isn't your average suburban garden.
It's the russian vine that's worrying me - its a big problem once its established, not because of its topgrowth, no - the problem is, it spreads through the ground ad infinitum, so that a border can be completely taken over by its roots. One I had to try and deal with (unsuccessfully, I might add) 20 years ago took up an area 20 feet wide by 10 feet from front to back in the ground...