Yes, it appears that a combination of cheaper (higher plastic content to rubber) tyre and a car not being used regularly can cause a tyre to become 'ovaled' a little bit like a flat spot.
There could be some of this with mine, but when on the wheel balancer, you could see that there was also a warping of the rim itself. So, even though the machine said everything was okay, you could see a movement of the wheel that would be amplified when on the car.
An Alloy wheel warped fixing service is very good to know about. I will try the dynamic wheel balancing first and when I'm ready to change the tyres, I might see if there is someone local that does this.