The production cross-section of the chi(c1)(3872) state relative to the psi(2S) meson is measured using proton-proton collision data collected with the LHCb experiment at centre-of-mass energies of root s = 8 and 13 TeV, corresponding to integrated luminosities of 2.0 and 5.4 fb(-1), respectively. The two mesons are reconstructed in the J/psi pi(+) pi(-) final state. The ratios of the prompt and nonprompt chi(c1)(3872) to psi(2S) production cross-sections are measured as a function of transverse momentum, p(T), and rapidity, y, of the chi(c1)(3872) and psi(2S) states, in the kinematic range 4 < p(T) < 20 GeV/c and 2.0 < y < 4.5. The prompt ratio is found to increase with pT , independently of y. For the prompt component, the double ratio of the chi(c1)(3872) and psi(2S) production cross-sections between 13 and 8 TeV is observed to be consistent with unity, independent of p(T) and centre-of-mass energy.