After a couple of nights sub-optimal sleep I decided to have a go at fitting some secondary glazing, and, not wishing to spend proper money on a rental house I came up with quite a pleasing solution: $100 worth of plastic (polycarbonate to be precise, specially designed crystal clear for windows) sheeting and draft excluding tape from the local DIY store.
The photo tells the rest of the story, but one nice thing: Because the window frames have multiple bevels, I didn't need to cut the sheets to size down the sides, I just chose something roughly right, knowing one of the bevels would do to buttress against. A relief since cutting this stuff smoothly is almost impossible.
I've tested noise with and without, and compared to the proper double glazing in the sitting room and it seems about as effective - in so much as you can tell with a free iPhone decibel meter anyway. :-)