...there is definitely a cost driver in favour of windows.
...which is that the windows environment is predicated on being a monitised platform, with paid for software. If you want to generate cost points at every level on IT (from software sales, through customisation, and out to support), and therefore pay staff, and build a business, then windows is the smart choice (as a supplier, the customer pays).
If you want to set up something for yourself, at minimum expenditure, with the ability to source free tools, and stitch them together to solve real tasks, then GNU/Linux has an awful lot to offer. Particularly with it's superior non-crippled network and security options, and it's more resource efficient footprint on servers.
I've constructed, deployed, maintained, and supported, both windows and *nix servers and networks. Neither does all the things that the other does, there are pro's and cons...but anyone who seriously thinks an open-source based network (servers and clients) are more expensive to run than a broadly equivalent windows network has been at the funny stuff.
Lots of small understandable tools, that can be deployed as a consistent whole, to achieve specific tasks, that can be easily customised, and efficiently deployed (resources, cycles, memory footprint, networking), beat the hell out of any monolithic, labyrinthine, dependency riddled windows application that I've ever had the displeasure to have to try to fix.
The point here is that the NHS is a large organisation, with a wide range of clinicians and other staff, and sod all chance of getting competent systems managers to every point of presence. It has a scale, and budget that should allow it to benefit from central provisioning, and maintenance. The customised, cut down, remotely maintained client-server model should be the best bet here (if with some local proxy/caching).
Way easier to achieve something good in this paradigm with GNU/Linux than windows, in my view. Open source tools should be as functional, more transparent, and less costly - both up front, in development, and in support. The difference is that you need to put together a team to do it, because there are not the layers of profit that there is in the proprietary sector that pays for all the "supplier knows best" that you are allowed to purchase at a substantial markup, and then locked into.