Visual Place Recognition (VPR) systems often have imperfect performance, affecting the `integrity' of position estimates and subsequent robot navigation decisions. Previously, SVM classifiers have been used to monitor VPR integrity. This research introduces a novel Multi-Layer Perceptron (MLP) integrity monitor which demonstrates improved performance and generalizability, removing per-environment training and reducing manual tuning requirements. We test our proposed system in extensive real-world experiments, presenting two real-time integrity-based VPR verification methods: a single-query rejection method for robot navigation to a goal zone (Experiment 1); and a history-of-queries method that takes a best, verified, match from its recent trajectory and uses an odometer to extrapolate a current position estimate (Experiment 2). Noteworthy results for Experiment 1 include a decrease in aggregate mean along-track goal error from ~9.8m to ~3.1m, and an increase in the aggregate rate of successful mission completion from ~41% to ~55%. Experiment 2 showed a decrease in aggregate mean along-track localization error from ~2.0m to ~0.5m, and an increase in the aggregate localization precision from ~97% to ~99%. Overall, our results demonstrate the practical usefulness of a VPR integrity monitor in real-world robotics to improve VPR localization and consequent navigation performance.