There has been an instance of
Plusnet blocking ports. In this case, it happened all of a sudden & the
http://www3.limewire.com:6346/ test showed "The page cannot be displayed" and "Cannot find server". After trying a port in the 49XX range this person was once again able to connect. This company has probably detected this person using p2p or just simply tried to prevent p2p use generally by blocking ports known to be used by p2p programs. Example
here. (edited to highlight isp name)