there will be no need for BBC news soon, when GB news starts - personally I can't waitYes, you need to be subscribed to Amazon Prime which will then allow you to stream the show on your computer, off a tab on the Amazon shopping home page. Go for Business Prime if you are VAT registered, because that gives you downloadable VAT invoices where relevant and warnings if the vendor is not VAT registered. You get Prime TV regardless.
I have both business and private Prime and can toggle between accounts. It makes keeping tabs of purchases and invoices much easier. Easier still is that I generally have Business account on Safari and private on Chrome browsers, so I just open whichever is relevant to the type of shopping I have to do.
Obviously a fairly fast internet account is needed to watch Prime TV without insufferable buffering interruptions. However you will find Prime TV to be much more efficient at streaming content than, say, a video to an equivalent quality on BBC News or YouTube.