This paper proposes an algorithm that enhances horizontal handover (HO) in dense wireless local area networks (WLANs), which is implemented in a software-defined wireless networking (SDWN)-based architecture. The algorithm considers the concept of user prioritisation, classifying the WLAN stations (STAs) into two categories representing high and low priorities respectively, and always attempts to guarantee the best quality of experience (QoE) to the high priority users. The architecture that implements the algorithm leverages the flexibility, programmability, and centralised nature of SDWN to efficiently manage the HO process. Moreover, the paper presents a performance evaluation campaign that demonstrates significant achievements against a state-of-the-art solution in terms of the provided QoE, throughput and delay. Finally, we discuss the importance of considering user prioritisation in a HO algorithm for dense WLANs.