While hollow core-photonic crystal fibres are now a well-established fibre technology, the majority of work on these speciality fibres has been on designs with a single core for optical guidance. In this paper we present the first dual hollow-core anti-resonant fibres (DHC-ARFs). The fibres have high structural uniformity and low loss (minimum loss of 0.5 dB/m in the low loss guidance window) and demonstrate regimes of both inter-core coupling and zero coupling, dependent on the wavelength of operation, input polarisation, core separation and bend radius. In a DHC-ARF with a core separation of 4.3 µm, we find that with an optimised input polarisation up to 65% of the light guided in the launch core can be coupled into the second core, opening up applications in power delivery, gas sensing and quantum optics.