You must keep paths clear - you aren't allowed to stack things in them, for instance. It must be possible to push a wheelbarrow down each one.
We try to mow the outside perimeter - at least when it's free of rubbish and not so overgrown we can't - plus a few of the larger paths. The rest are the shared responsibility of the neighbouring plotholders to keep clear.
We don't know which things are designated paths and which are not. Originally, the site was all full plots, and there were paths around blocks of four. These are usually discernible from the site map. Now there are many half and quarter plots, so new paths have been created - every plot can be accessed somehow. If in doubt, work it out among yourselves, or perhaps the Council can assist you.