Mine never had plagio, but she did tend to look to the left almost exclusively when she was very tiny. We took her to a cranial osteopath when she was about 3 months or so, because she kept going on nursing strike, and it was discovered that she had a really stiff neck and a twist in her spine due to her birth. She got stuck at almost full dilation because she was facing the wrong way. Her head was bent back and her body got corkscrewed by contractions. The osteopath said that because of this, her body preferred to be banana-shaped, with her back arched and head tilted backwards - and at that moment I realised that that was EXACTLY the position she slept in, on her side, in a curve. After that realisation, I had full faith in the technique, and she found it so relaxing that she fell into a deep sleep while she was being treated.
The breastfeeding didn't improve (turned out it was down to a different issue), but she stopped lying like a banana and definitely had more range of motion in her neck. It only took three treatments.
I think all babies should visit a cranial osteopath after birth, no matter how easy it was. The forces exerted on your body during the birthing process can actually stay with you for life!
It's a fantastic place to start as it is nothing more than gentle touch - if it doesn't help then there are other options to try. The flat spot should correct itself as he spends less time on his back, but it's important that his neck is treated for his comfort, and a cranial osteopath should be able to do this.
I believe the NHS would only treat the most severe plagiocephaly cases. Our sessions with the osteo were about £30 each I think.