A wireless telecommunications system in which downlink communications are made using a radio interface that spans a system frequency bandwidth (host carrier) and supports at least some communications from a base station to least some terminal devices within a plurality of restricted frequency bands (virtual carriers) which are narrower than and within the system frequency bandwidth. A terminal device conveys an indication of its identity, to the base station during an initial connection procedure as the terminal device seeks to access the radio interface. The terminal device and the base station both determine a selected restricted frequency band from among the plurality of restricted frequency bands based on the identity of the terminal device in the same way. Thus the terminal device and base station select the same restricted frequency band and can accordingly configure their respective transceivers to allow downlink communications between them within the selected restricted frequency band.