I have collated a brief list of German tv channels you can watch online in the UK. It might be useful to others, so here it is. Some programmes may not work due to legal restrictions, but I am hopeful that this will change in the future (EU single market and all that).
There are some streaming apps that claim to work well – if you choose to use them (not sure about legality of some of them).
Deutsche Welle: mainly educational content and documentaries
ARD Mediathek: Germany’s first public channel
Arte: German and French arts and culture channel
MDR Mediathek: Regional public channel (central)
NDR Mediathek: Regional public channel (north)
RTL: private channel, offering entertainment and edutainment
VoxNow: private channel, offering entertainment and documentaries
ZDF Mediathek: Germany’s second public channel