Ground displacements due to ocean tide loading have previously been successfully observed using Global Positioning System (GPS) data, and such estimates for the principal lunar M2 constituent have been used to infer the rheology and structure of the asthenosphere. The GPS orbital repeat period is close to that of several other major tidal constituents (K1, K2, S2); thus, GPS estimates of ground displacement at these frequencies are subject to GPS systematic errors. We assess the addition of GLONASS (GLObal NAvigation Satellite System) to increase the accuracy and reliability of eight major ocean tide loading constituents: four semi-diurnal (M2, S2, N2, K2) and four diurnal constituents (K1, O1, P1, Q1). We revisit a previous GPS study, focusing on 21 sites in the UK and western Europe, expanding it with an assessment of GLONASS and GPS+GLONASS estimates. In the region, both GPS and GLONASS data have been abundant since 2010.0. We therefore focus on the period 2010.0–2014.0, a span considered long enough to reliably estimate the major constituents. Data were processed with a kinematic precise point positioning (PPP) strategy to produce site coordinate time series for each of three different modes: GPS, GLONASS and GPS+GLONASS. The GPS solution with ambiguities resolved was used as a baseline for performance assessment of the additional modes. GPS+GLONASS shows very close agreement with ambiguity resolved GPS for lunar constituents (M2, N2, O1, Q1) but with substantial differences for solar-related constituents (S2, K2, K1, P1), with solutions including GLONASS being generally closer to model estimates. While no single constellation mode performs best for all constituents and components, we propose to use a combination of constellation modes to recover tidal parameters: GPS+GLONASS for most constituents, except for K2 and K1 where GLONASS (north and up) and GPS with ambiguities resolved (east) perform best.