I couldn't help but chuckle reading through the thread at how everyone else did the river split using fancy spatial tools. I just used the data provided, added some context from the real world, and got the task finished quick so I can get out from behind the keyboard and into a pub!
I don't normally post my answers to these but I thought this one might be of some use to someone. I decided to have a go a building a custom polygon that intersected the Thames and took only the bit north of the river. Hopefully there is an easier way of doing this than my method! Looking forward to rolling that out as a question to my tutor in the spatial analytics class at inspire.