I don't think you need to worry about the torticollis as some physiotherapy should fix it but you do need to get it seen to. Don't bother with the HV, she can't refer you for physiotherapy (or can they?) So just go straight to doc and tell them he doesn't turn head one way. My son had torticollis and developed plagiocephaly which the Nhs doesn't treat and largely doesn't acknowledge. I've learned to be a little hard nosed and push to get the right treatment for him. I would say that you shouldn't just accept what the docs say but take their advice and do your own research before deciding what's right for you.
The physio made a huge difference within just days of starting it for us. Unfortunately at 5 months he still had a flat spot and an symmetrical face so we decided to get a helmet. The helmet companies say to try repositioning up until about 5 months. They can also take measurements to assess the flattening and whether it is worth having a helmet. It's not right for everyone but we are so glad we did it. He wore it for 3 months ( we just finished 2 days ago) and I'm so pleased with results. As you have to pay for it yourself, there is a charity that helps people called HeadStart4Babies (I think, I'll check).
But don't worry about that yet, you need to get the torticollis sorted first or you'll struggle with repositioning to work on the head shape. The Nhs will tell you the shape will fix itself or that hair will cover it. I feel they are biased as they consider it cosmetic but they should treat the torticollis.
Oh dear, having written all that, I've reread your reply. If he can turn it, then it may not be torticollis, I don't know. I'm not sure if there are different severities, my son couldn't't turn at all even when the doc pushed his head over (gently!). I would still get it checked out so you have peace of mind and can focus on the flat head.