Have you looked up folks in leadership or decision making roles at NHS Digital on LinkedIn and reached out to them directly?

Simon Bolton is their CEO equivalent. firstname.lastname@ nhsdigital.nhs.uk

https://twitter.com/simonrbolton

This is a sales job. Sell them aggressively (in the sense that it solves a problem, not necessarily monetarily). Failing to get traction with NHS Digital, reach out to potential non profit charities that are advocates for cancer screening and womens’ healthcare. Let them be the force multiplier asking why a solution you propose isn’t used or provided by the NHS. Let the value proposition speak, and do not be apologetic about being loud about it.