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It is still poorly constrained how the densest phase of the interstellar medium varies across galactic environment. A large observing time is required to recover significant emission from dense molecular gas at high spatial resolution, and to cover a large dynamic range of extragalactic disc environments. We present new NOrthern Extended Millimeter Array (NOEMA) observations of a range of high critical density molecular tracers (HCN, HNC, HCO+) and CO isotopologues (13CO, C18O) towards the nearby (11.3 Mpc), strongly barred galaxy NGC 3627. These observations represent the current highest angular resolution (1.85"; 100 pc) map of dense gas tracers across a disc of a nearby spiral galaxy, which we use here to assess the properties of the dense molecular gas, and their variation as a function of galactocentric radius, molecular gas, and star formation. We find that the HCN(1-0)/CO(2-1) integrated intensity ratio does not correlate with the amount of recent star formation. Instead, the HCN(1-0)/CO(2-1) ratio depends on the galactic environment, with differences between the galaxy centre, bar, and bar end regions. The dense gas in the central 600 pc appears to produce stars less efficiently despite containing a higher fraction of dense molecular gas than the bar ends where the star formation is enhanced. In assessing the dynamics of the dense gas, we find the HCN(1-0) and HCO+(1-0) emission lines showing multiple components towards regions in the bar ends that correspond to previously identified features in CO emission. These features are co-spatial with peaks of Halpha emission, which highlights that the complex dynamics of this bar end region could be linked to local enhancements in the star formation., Comment: 25 pages, 12 figures; accepted for publication in MNRAS