Re: "improve productivity in an organisation severely short of staff"
I'd have thought the best thing to do with regard to "digitalising" the NHS would be not to build some huge monolithic system and drop it onto the entire NHS all at once, but the spend a few years getting it right at a single Trust. Spend whatever it takes to make it work and demonstrate it working effectively to the rest of the NHS such that they are clamouring to implement it. They could even take two best (note: not cheapest) bidders, and give them a Trust each to work with and see what comes out best/quickest/most efficient.
Or better yet, buy in the talent at market rates and build it in-house, specifically for the UK as a whole such that maybe later they could sell systems to other health agencies around the world. That way, they'd not even be tied to a specific OS if they choose.