High-performance interferometers, gyroscopes, frequency combs, quantum information experiments and optical clocks rely on the transmission of light beams with the highest possible spatial and polarization purity. Free-space propagation in vacuum unlocks the ultimate performance but becomes impractical at even modest length scales. Glass optical fibres offer a more pragmatic alternative, but degrade polarization purity and suffer from detrimental nonlinear effects. Hollow-core fibres have been heralded for years as the ideal compromise between the two, but achieving high modal purity in both spatial and polarization domains has proved elusive thus far. Here, we show that carefully designed, low-nonlinearity hollow-core antiresonant fibres can transmit a single pair of orthogonal polarization modes with cross-coupling on the scale of 10 – 10 m – 1 ; that is, orders of magnitude lower than any other solution. This free-space-like optical guidance can immediately provide a leap in performance for photonics-enabled sensors and instruments.