London power meltdown
The EV problem isn't just Royal Mail in London. Lots of stuff has had to be moved outside the M25 due to lack of power availability.
The overload problem in London is severe and ongoing, as is the lack of maintenance - those exploding footpaths that happen every so often are power cables letting go due to sustained overload.
As for vehicles: Forget Tesla. There are a few (very few) electric vans (Nissan have the NV2000, PSA have a couple, etc etc) and there's no secondhand market for those because their owners are hanging onto them for grim death due to the low operating costs.
Any comments about dearth of range of vehicle types misses the point that outfits like RoyalMail tend to run tens of thousands of identical types and given the type of use these vehicles get, there's likely to be a lot of potential for pollution reduction in an EV with a very small 1-2kW "range extender" hybrid engine (or even something like a 1-5MW local generator their EVs can plug into at the depot instead of relying on National Grid.
All the hoopla is on passenger vehicles - precisely because they're a low demand environment - but the real gains to be had are in vans and light commercials.
Comments about fuel tax are germane: The UK government currently gets more than £65billion from excise duty and various taxes from road fuel and spends less than 1/4 of it back on roads. It won't give up that income without a fight. You can expect homecharging to stay exempt under the excise equivalent exemption of "2000 litres of road fuel per year per premises" for non-commercial production but expect to start seeing excise costs on roadside charging stations soon.