In multichannel systems, acoustic time delay estimation (TDE) is a challenging problem in reverberant environments. Although blind system identification (BSI) based methods have been proposed which utilize a realistic signal model for the room impulse response (RIR), their TDE performance depends strongly on that of the BSI, which is often inaccurate in practice when the identified responses are under-modelled. In this paper, we propose a new under-modelled BSI based method for TDE in reverberant environments. An under-modelled BSI algorithm is derived, which is based on maximizing the cross-correlation of the cross-filtered signals rather than minimizing the cross-relation error, and also exploits the sparsity of the early part of the RIR. For TDE, this new criterion can be viewed as a generalization of conventional cross-correlation-based TDE methods by considering a more realistic model for the early RIR. Depending on the microphone spacing, only a short early part of each RIR is identified, and the time delays are estimated based on the peak locations in the identified early RIRs. Experiments in different reverberant environments with speech source signals demonstrate the effectiveness of the proposed method.