I'm pretty late to this story, but let me clear up some misunderstandings for posterity's sake:
Disclosure: I've been involved in this effort for at least ten years, I'm head of ICT for one of the UK Copyright Libraries (National Library of Wales), and this story goes way back to the Primary Legislation passed by the UK in 2003, and we've been working on the practicalities of this since before that legislation was passed.
* Yes, Internet Archive and others have been archiving web sites for many years. We're using their software for capturing.
* We've been collecting and archiving web sites by agreement with the web publishers for years via the UK Web archive project.
* What's different here is that the secondary legislation has been passed (in March) that has given the UK copyright libraries the mechanism (agreed with publishers) to extend legal deposit to digital publications, which includes websites.
* This gives the legal deposit libraries the right to add to the national legal deposit collections (the collection of all published material for the UK) digital publications, including ebooks, ejournals and websites.
* Until the 6th of April 2013, we did not have the right (under normal copyright law) to take a copy of websites without permission. Previously we had to request a written agreement from each website we archived to take a copy - obviously this does not scale very far.
* Under the new legislation, we will be taking periodic copies of the entire .uk domain and other websites in other domains which fall under the regulation (territoriality has been difficult to define, as you may imagine).
* The difference between us and the Internet Archive is intended to be that given the status as a national collection, the material that we collect is intended to be available in perpetuity. Our print collections go back centuries, and the intention is that the digital material we collect now will also be available in centuries to come. You can read about the distributed redundant storage here.
TL;DR : this is a legal thing, not a technical thing, and it's about a lot more than websites.