I would focus on private first. Completely independent is even better - do independent physiotherapists and practices exist? Leave BUPA and the NHS for later. Reasons:
1) The product is a quality one, not a value one. The focus of the people who buy for the NHS is to save money (their incentive to provide better care mainly ends up in high visibility areas such as trauma). I don't mean to sound negative. I think the NHS is great for what it does for us, but that's how it is. On the other hand, the sole purpose of private practices is to provide a better service than the NHS.
2) Once you have one private practice using your system, other private practices will look bad if they continue using just printed instructions, giving them a direct incentive to buy. This is helped because...
3) Patients talk to each other, especially so here because presumably there is a correlation between the subset of patients who go private and those with a particular socio-economic status. Patients will hear about the better product from friends and expect the same from their own therapists.
4) Validation from a smaller segment is incredibly valuable in moving up. A proven track record with independents will help convince BUPA (imagine trying without this). A proven track record with BUPA will help convince the NHS (and presumably the NHS won't accept it unless it directly reduces their costs or the expected quality of care rises such that your product is required).
Also, get this book: http://www.amazon.co.uk/Crossing-Chasm-Marketing-Technology-...
Edit: fixed typos.
It's tricky because simply being a startup is a brand negative as you try to sell to increasingly conservative customers.
There's books about it. Here's one:
https://www.amazon.co.uk/Crossing-Chasm-Marketing-Technology...