It looks like the law stems from European Directive 2001/29/EC (2001) [2][3]. That directive isn't law in itself, it's an instruction for the EU member states to implement law to deliver that directive (in fact, the UK were initially convicted of failing to implement it by the 2002 deadline).
At a guess, the relevant law is the Copyright, Designs and Patents Act 1988, Section 24 [4]:
Secondary infringement: providing means for making infringing copies.
(1)Copyright in a work is infringed by a person who, without the licence of the copyright owner—
(a) makes,
(b) imports into the United Kingdom,
(c) possesses in the course of a business, or
(d) sells or lets for hire, or offers or exposes for sale or hire,
an article specifically designed or adapted for making copies of that work, knowing or having reason to believe that it is to be used to make infringing copies.
[1] http://www.gazettelive.co.uk/news/teesside-news/kodi-box-cou...[2] http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A6...
If that's actually the case, then it's hard for me to see how selling the fully-loaded Kodi box is more illegal than selling a computer with an internet connection. After all, there's third party software for computers that give access to pirated content as well, right?
edit: Ah, I guess I misunderstood the article. Some people are selling boxes preloaded with Kodi, and other people are selling boxes preloaded with Kodi+the third party apps, I guess?