The prevalence of mobile devices especially smartphones has attracted research on mobile content delivery techniques. In this paper, we propose to take advantage of the storage available at wireless access points to bring content closer to mobile devices, hence improving the downloading performance. Specifically, we propose to have a separate popularity based cache and a prefetch buffer at the network edge to capture both long-term and short-term content access patterns. Further, we point out that it is insufficient to rely on a device's past history to predict when and where to prefetch, especially in urban settings; instead, we propose to derive a prediction model based on the aggregated network-level statistics. We discuss the proposed mobile content caching/prefetching method in the context of the MobilityFirst future Internet architecture. In MobilityFirst, when mobile clients move between network attachment points (e.g., Wi-Fi access points), their network association records are logged by the network, which then naturally facilitates the network-level mobility prediction. Through detailed simulations with real taxi mobility traces, we show that such a strategy is more effective than earlier schemes in satisfying content requests at the edge (higher cache hit ratios), leading to shorter content download latencies. Specifically, the fraction of requests satisfied at the edge increases by a factor of 2.9 compared to a caching only approach, and by 45% compared to individual user-based prediction and prefetching.