sounds like a potential DNS issue, most internal stuff is using IP address so doesn't need to do any dns resolution. your phone and other machine would have initialised their DNS config when you connected whilst your laptop probably has a lease set so it only refreshes every so often. hence it suddenly starting working.
if it happens again try hitting bbc directly using IP
http://212.58.246.94/ ( you shoudl get a bbc branded 404 error page )