Taming of the Hedge

The beech hedge which is our roadside boundary was in dire need of a haircut as it was leaping out and catching passing double decker buses. Being on a main A road just on the brow of a hill we decided not to risk life and limb to do it ourselves. 
Today a great team of gardeners came to do the job with hazard lights flashing. The traffic all managed to avoid mishap. The whole thing is a great improvement. and I dare say the bare bits will sprout new leaves in the spring.
The next thing is to tackle the horrid strip of weed infested grass between the road and our new smaller hedge. Running the mower around next to the road is no fun so it needs some fast growing ground cover. Leaving it as a meadow isn't an option as we can't see past to dodge the traffic whizzing over the hill as we pull out of the driveway. All suggestions gratefully received. I've started at one end with vinca and wild strawberries with some nasturtiums for colour but there is quite a lot of it.