I'd like to add an option to shrink the left-hand site navigation but it'd be a lot of work - basically it'd require reworking pretty much the entire layout of the map page. I'll try and do it as part of a wider rework of some parts of the design but it won't be any time soon I'm afraid.

You can make the cycle.travel browser window full-screen by using the button in the map switcher (top right) though that won't change what appears in it.

Not directly answering the original question, but may be useful for iOS users:

In iPhone/iPad Safari, tap the “Aa” then “hide toolbar” to eke out a bit more screen real estate.

(This may require a recent iOS version)