As I have said elsewhere assuming the tool works as I have set out there it seems to be very difficult to argue that its use in the UK (and that would include picking up material from UK sources) would not infringe copyright.* I'm also rather sceptical having looked at the WebCite's FAQ's that their basis for arguing that it's legal in the US is based on a 2006 first instance judgement - in terms of internet law that sounds rather like arguing that a medical procedure is safe because archaeological evidence shows it was used in the Neolithic era. However, you've presumably got better access to advice on that topic than I have.
*There are some interesting arguments based on the location of Web-Cite's servers, admittedly,
no subject
*There are some interesting arguments based on the location of Web-Cite's servers, admittedly,