No idea what it costs, but GDS[1] is doing a pretty good job on http://gov.uk. My guess is that only the savings on closing hundreds of sites [2] justifies it. Maybe it also prevents some of the uk citizens from not going nuts while trying to do gov business online ;)
It's an amazing site not just for being 'clean' and functional, but also for how much effort they've put into actually making the information easy to understand and read. E.g consider the page on VAT rates (that's roughly like sales tax for the Americans here):
[1] http://digital.cabinetoffice.gov.uk/ [2] https://www.gov.uk/government/news/hundreds-of-government-we...