"We intend to open source our codebase once the first release is finalised. The documentation accompanying that release will supersede this paper."
and from https://www.ncsc.gov.uk/blog-post/security-behind-nhs-contac...,
"The Secretary of State has also committed to making the source code open source. That may not happen immediately on release because the fabulous NHSX development team are all working hard on getting the product ready. But it will happen."
Sounds like there is an intention to deliver on the source. Bigger question is whether the server side is open sourced (as clearly that has limited value for verifying what is happening remotely).