Models of animal signalling stress that among unrelated individuals the transfer of honest information normally requires that signals are costly, and costly in a way related to the true information revealed by the signal. In the absence of such a cost, `cheats', that lie about their states or needs, are able to evolve and exploit the preferences of receivers. We show here that spatial constraints imposed on the interactions between signallers and receivers favour honest signalling even in the absence of any costs: `islands' of honesty coexist in `seas' of dishonesty. The extent to which honest or dishonest strategies are favoured, is shown to depend upon the relative payoffs from signalling and receiving. As the receiving component of fitness becomes greater than the signalling component of fitness, as might be true in `life-dinner' type interactions, honesty is increasingly favoured. In addition, in spatial populations, honesty can be favoured locally even when the mean global payoffs to honesty are lower than the mean payoffs to dishonesty. Our model provides a general framework for analysing signals in spatially structured populations and might therefore apply to signalling in both natural and cultural situations.