We study the quantum melting of quasi-one-dimensional lattice models in which the dominant energy scale is given by a repulsive dipolar interaction. By constructing an effective low-energy theory, we show that the melting of crystalline phases can occur into two distinct liquid phases having the same algebraic decay of density–density correlations but showing a different non-local correlation function expressing string order. We present possible experimental realizations using ultracold atoms and molecules, introducing an implementation based on resonantly driven Rydberg atoms that offers additional benefits compared to a weak admixture of the Rydberg state.