Preventing weed growth on soil wall/slope

Hi all, 

My allotment site is on a slope. My individual plot is higher on one long side than the other. From the weedy grassy path that runs between our plot and the neighbours', it's about a foot or more step down to my plot. That means some of my beds have a weedy wall with grass that grows down from the path. It is hard to strim and the overhanging grass causes a lot of pest damage to things growing in those beds 

Any ideas to practically mulch/cover/control the little wall/slope that won't be a complete haven for slugs etc?

Thanks!

Using the Permaculture Principle of "The Problem is the solution",  the Problem is the Path. 

or, with my Dr. Veggie M*D hat on, the symptoms (weedy wall, overhanging grass, pest damage) lead us to a diagnosis that if the  Path wasn't grass, the symptoms would be cured/eased. 

You said you have paving slabs,  can you put these on the path to keep the grass under control. Would your neighbour have any objections? Would save work on strimming.