This has been coming for a long time. Government contract pricing is based on the same basic principle, that suppliers in "cheaper" parts of the country have lower overheads.
But practical implementation across the public sector is quite another thing and I foresee major problems. Government tends to create rather false geographic areas when doing things like this. Someone mentioned mobile civil servants. At the time of the enforced move to AbbeyWood we were entitled to "Excess Rent Allowance" to cater for price differentials when buying/renting a house at the new station (an important consideration when you're already on income support due to low salary). The Treasury skewed the figures to somehow conclude Bristol was less expensive than the likes of Colchester, so very few qualified for ERA. Yet the like for like house prices were higher, and escalating quickly as 6,000 families moved into the area. Prices in the likes of St Pauls were indeed very low - and the Treasury took full advantage of this in their calculations.
However, I foresee one good thing in MoD, if they are brave enough. In certain establishments many posts are over-graded to permit an artificially high salary for the job. This results in MoD having some very senior people who are actually grossly inexperienced. Time to resurrect and strictly implement the Treasury agreed Grade Descriptions. That would stop most promotions at AbbeyWood for the foreseeable future! A far easier way to save on the salary bill. In one section there, they have a One Star doing a job the vast majority of his staff left behind 4 or 5 promotions ago.