@LukeM For what it's worth, I've used the buffer tool in the past to turn the line into a really thin polygon. Then you can use the spatial process to remove the line from the trade area and then poly split to split the 2 separate parts into their own rows. Your solution is simpler, but this method will return the 2 separate pieces of the polygon which is sometimes useful.
I opted to find the nearest bar on the other side of the river as the crow flies. Shame I don't have Tom Tom, because it would be a shorter stumble home from the Mayflower than the Angel, unless you fancy a swim.