This article introduces a novel family of decentralised caching policies, applicable to wireless networks with finite storage at the edge-nodes (stations). These policies, that are based on the Least-Recently-Used replacement principle, are here referred to as spatial multi-LRU. They update cache inventories in a way that provides content diversity to users who are covered by, and thus have access to, more than one station. Two variations are proposed, the multi-LRU-One and -All, which differ in the number of replicas inserted in the involved caches. We analyse their performance under two types of traffic demand, the Independent Reference Model (IRM) and a model that exhibits temporal locality. For IRM, we propose a Che-like approximation to predict the hit probability, which gives very accurate results. Numerical evaluations show that the performance of multi-LRU increases the more the multi-coverage areas increase, and it is close to the performance of centralised policies, when multi-coverage is sufficient. For IRM traffic, multi-LRU-One is preferable to multi-LRU-All, whereas when the traffic exhibits temporal locality the -All variation can perform better. Both variations outperform the simple LRU. When popularity knowledge is not accurate, the new policies can perform better than centralised ones.