The first step to soundproofing windows is minimising any air gaps with foam or sealant. You'll want to add the foam stripping around the window and where it meets the sill. This foam gets compressed when the window is closed.
Sealing any gaps would be a good start (use dense rubber strip, not the light holey stuff). It made a huge difference when I did that on my front door. I did it to stop air leaking heat in and out, but was immediately surprised at how much the outside sounds dropped too.
Secondary glazing, similar to Magnitite should help. But whatever you use needs to be a material that is dense, since it is the density of the material that absorbs sound, not the shape or its thickness. I therefore doubt that the twin wall carbonate will be effective enough as it doesn't have the density to absorb the sound. However, it is relatively cheap, so you could give it a go and see if it blocks enough.
We just sound-lowered our bedroom, and found that much of the external sound was coming through the ceiling. If you have plaster ceilings that entry point will be worth considering too.
We had double glazed windows fitted (for temperature control) and they do lower the sound substantially. I had sound insulation batts put in the bedroom ceilings (with heat insulation on top) and that lowered the sound heaps. We can still hear the outside world if it's loud enough, but not enough sound gets through to stop us sleeping now. - TedBear
If the majority of the sound is coming through the window I suggest using a Bastion 1200 x 600 x 50mm XPS Multi-Use Insulation Foam Board. You can easily cut this foam board to the interior size of the window and push fit into the frame of the window to give you a 100 percent sound seal. When it comes time to take it out you can simply use the back end of a spoon and pop it out. This is a temporary fix and will not cost you a lot. It won't be pretty but I'm sure you can find a spot to hide it away for the day until it is time to go to bed. - redracer01