Applying these calculations on a dataset for locations in england and wales generates this map (which exactly matches the hex centres in the first map above with hexagons with sides of 1 degree).
PS My experimental workbook for the above examples is too big for Tableau Public so I can't link to it here. But I have a workbook that just uses the postcode locations (of which there are about 2.5m) that illustrates the way hex bins work. It is a little dull as the density of postcodes is basically an unreliable proxy for population density. But the workbook is here for those who want to check out the formulae or some simple analysis of how UK postcodes work.