Soundproofing windows against air traffic noise
First, figure out how the majority of noise is getting into the interior.  Is it really coming through the windows? Or is it coming through the roof and ceiling and walls?

Windows are the hardest to sound deaden, but you imply you are good with acoustic foam on the windows?!  What about bricking (in a removable way) over the window?

An existing space can be quieted substantially with heavy draperies from ceiling to floor.  Not just on the windows, but on the walls.  

A drop ceiling installed under an existing ceiling also helps.  That also allows placement of additional insulation.

No idea what the limits are for UK rentals, but they seems to be a lot more loosey-goosey than in the U.S.!