Avoiding???

I don't know Em.  Sounds like she's avoiding pain or pressure from somewhere.  Trainer needs to step in here .... anytime trainer!!!  []

Ah, perhaps, but why would she go sideways, surely she'd limp or buck or something? Instead she just goes sideways, it seems to be that she wants to go one way and nothing is going to stop her, like sneaky napping? I don't know. 

I tend to agree with Hunter.  It sounds like a soundness issue.  Standardbreds will often  "get on one line" "Bear out" or Bear in" when they have a soundness issue.  The pain comes with the faster gaits because the foot strikes the ground harder and that percussion goes up the leg through the joints.

If you have any friends in the racing business, they just might  be able to help you.  If they can't, they should be able to point you to a good trainer or a horse vet who should be able to help.  I am thinking this probably stems from the lameness she exhibited after her "paddock shenanigans".  An Equine Chiropractor might be able to help, also.

Keep us posted.

surely she'd limp or buck or something

maybe it's her mouth.  Or her neck or back...  Maybe bucking would hurt worse.  sounds like a nice horse. []

Well, she has not exhibited any more turning strangely whilst cantering, She has always been a bit wiggly to canter but the vet said that was due to her strong butt muscles, which given the size of it, I do not doubt. She is sound in both in-hand trot and ridden trot. She is barefoot, but I doubt this has much to do with it seeing as she is only ridden on soft surfaces. It could be teeth, when we have the vet out to castrate Storm (AT LAST, he has descended at 8 months!) I will ask him to have a look! Cheers guys =]    

This is very difficult to deal with from this side of the pond, but here's a try...
 
You say she's ploughing through her bit and avoiding leg.  Okay, how is she bridling when you are experiencing this with her?  Sounds to me like, though you have contact, you don't have control.  A thick-necked Cob is going to be difficult to bridle, however without it, you are depending on her good graces for obediance.  Try lowering your hands and shaking the bit whilst this is going on.  You must release some pressure and yet not throw her away.   If you do it right, shaking the bit will result in her dropping her head and submitting to the bit.  It's a sharp side to side movement in a kind of figure-of-eight, though not at all sawing at her mouth.  You're shaking the bit, not abusing her tounge and bars.  If she doesn't submit, try holding your hands a bit lower and doing it again.  Remember, you are not sawing, but shaking and it must be sharply done.  Be careful though as she might throw her head a time or two.  You don't want a hard knock in the face.  A good place to practice this is in a closed paddock or arena with as few distractions as possible.
 
If she reacts positively to this technique, it will be only briefly at first.  Over time she will remain bridled longer.  With a heavy neck, the old girl isn't going to like this as she will be sore if you hold her in this position too much.  It's one of those things that must be gradually worked into.  Time is the cure for all troubles, Luv. 
 
Also, she might slam to a halt the first time you do this.  Many horses do.  Some even rear up, but this is usually because the handler used way too much pressure.  So, watch your seat, and be prepared for whatever reaction she might have.
 
Sounds like the old girl has just gotten used to being alpha mare and needs to be put back in her place a bit.
 
All the best.

Hi, sorry the reply has been so long in coming, things have been extremely busy this side of pond! I tried bringing her down onto the bit using shaking and figure-of-eight technique but she just pulls her head up and ignores the bit, even when its quite a strong bit. She also naps quite badly when out hack, and although I am a competent rider, it is proving a problem as I do have to multi-task out on hacks (gates, answering the phone ect, ect.) And she just goes, ahaha f*** off I'm going home, leaving me in a pickle. I was using a Weymouth bit as a gag due to lack of alternatives and she actually behaved worse in it. My theory was she was lifting her head to avoid the pressure on her mouth and poll, so am now going to ride her in a French Link Snaffle. Lack of local grazing means she isn't ridden regularly enough. Anyway, will let you know how it goes. Thank you for your time