There are a host of applications in communications, sensing, and science, in which analogue signal transmission is preferred over today’s dominant digital transmission. In some of these applications, the advantage is in lower cost, while in others, it lies in superior performance. However, especially for longer analogue photonics links (up to 10 s of km), the performance is strongly limited by the impairments arising from using standard single-mode fibres (SSMF). Firstly, the three key metrics of analogue links (loss, noise figure, and dynamic range) tend to improve with received power, but this is limited by stimulated Brillouin scattering in SSMF. Further degradation is due to the chromatic dispersion of SSMF, which induces radio-frequency (RF) signal fading, increases even-order distortions, and causes phase-to-intensity-noise conversion. Further distortions still, are caused by the Kerr nonlinearity of SSMF. We propose to address all of these shortcomings by replacing SSMFs with hollow-core optical fibres, which have simultaneously six times lower chromatic dispersion and several orders of magnitude lower nonlinearity (Brillouin, Kerr). We demonstrate the advantages in this application using a 7.7 km long hollow-core fibre sample, significantly surpassing the performance of an SSMF link in virtually every metric, including 15 dB higher link gain and 6 dB lower noise figure.