Lepton flavour universality is tested by measuring the ratio of branching fractions of B+ → K+μ+μ− and B+ → K+e+e− decays, RK. The measurement is performed in the di-lepton mass squared region 1.1 < q2 < 6.0 GeV2, using approximately 5 fb−1 of data collected with the LHCb detector between 2011 and 2016 at centre-of-mass energies of 7, 8 and 13 TeV. The value of RK is measured to be RK = 0.846 +0.060−0.054 (stat.) 0.016−0.014 (syst.), where the first uncertainty is statistical and the second is systematic. This result is compatible with the Standard Model expectation at the level of 2.5 standard deviations. This analysis has an uncertainty 36% smaller than previous measurements of this quantity. The analysis is performed using B+ → K+J/ψ(μ+μ−) and B+ → K+J/ψ(e+e−) decays as control and normalisation channels. Innovative calibration techniques and cross-checks are employed. The cross-checks demonstrate that the electron detection efficiencies are well understood, and that the LHCb detector can be used to study precisely and reliably the decays of beauty mesons to final states with electrons.