In this paper, we propose a joint single-base localization and communication enhancement scheme for the uplink (UL) integrated sensing and communications (ISAC) system with asynchronism, which can achieve accurate single-base localization of user equipment (UE) and significantly improve the communication reliability despite the existence of timing offset (TO) due to the clock asynchronism between UE and base station (BS). Our proposed scheme integrates the CSI enhancement into the multiple signal classification (MUSIC)-based AoA estimation and thus imposes no extra complexity on the ISAC system. We further exploit a MUSIC-based range estimation method and prove that it can suppress the time-varying TO-related phase terms. Exploiting the AoA and range estimation of UE, we can estimate the location of UE. Finally, we propose a joint CSI and data signals-based localization scheme that can coherently exploit the data and the CSI signals to improve the AoA and range estimation, which further enhances the single-base localization of UE. The extensive simulation results show that the enhanced CSI can achieve equivalent bit error rate performance to the minimum mean square error (MMSE) CSI estimator. The proposed joint CSI and data signals-based localization scheme can achieve decimeter-level localization accuracy despite the existing clock asynchronism and improve the localization mean square error (MSE) by about 8 dB compared with the maximum likelihood (ML)-based benchmark method.