I would imagine the BL have referenced archive.org work extensively
They've actually worked closely with the Internet Archive for many many years. This includes commissioning IA to conduct crawls for them of government sites.
Both the BL and IA are members of the International Internet Preservation Consortium (IIPC see: http://netpreserve.org./ Both are very familiar with what the other is doing in this space.
So why not let IA do all the work? There are several reasons. Part of it is that the BL is responsible for web archiving as far as British cultural heritage is concerned. Relying on a foreign entity to handle it is questionable as they would not be able to enforce any/all policies they might need on IA. You can certainly contract the IA to crawl for you, but it will be on their terms.
However, there is also a question of redundancy. If multiple institutions, all over the world, are all engaged in web archiving, the ultimate result will be much better coverage and resilience. From my experience in dealing with the Internet Archive, this is something they support. Ever since I got involved in web archiving, 10 years ago, the Internet Archive has been a strong support of national libraries, archives and other interested parties doing their own web archiving.
That is why the IIPC was formed. So we could share knowledge and pool resources where useful while each institution follows its own path in web archiving.