Looking again at CIFPA's list of the UK's five biggest libraries, I note that at least four of them appear to be (in some way quite new).
The one I know best is of course Wembley Library, now the third most visited in the country with almost 1.4 million visits. That is a stark contrast to the old Brent Town Hall library it replaced, which had about 200k visits at the time it closed. Wembley Library was of course newly opened as a custom built facility in 2013.
Birmingham Central Library was opened at vast expense in 2013. Manchester underwent a major refurbishment prior to reopening in 2014. Woolwich Library opened I am not sure when, but I think it was quite recently. I believe they all attracted a lot of negative publicity until they actually opened.