The Tesla Powerwall is a toy and they were late to the market with it. There are more robust and cost effective battery back up systems from real companies such as Bosch, Siemens, LG, BYD, etc. They're not as pretty, but….
Solar insolation is about 1kW/m2 at the top of the atmosphere, but lower at ground level. Solar panels are right around 20% efficient so it takes a fair roof full to power a car. Tesla's solar shingles are packed far less densely on a roof than the garden variety panels which means even less generation on a given roof with solar shingles
The upside of turning Postman Pat's car to electric is that like many people's cars, it's going to be sitting all night so it doesn't need a dc fast charger. A level 2 charger should be just fine. Mail cars don't travel long distances, so they don't need massive batteries. While London may have an electrical capacity issue durning the day, past business closing times, there may be plenty available for car charging. Using a few postal vehicles might be a great setting to test out some smart charging regimes where cars talk to the grid and modify their charging times/rates according to power availability.
There is no universal law that states the Post has to convert every delivery car everywhere in the country to electric all at once or even that they all have to be electric. They can ease into it and start with areas where it makes the most sense. The constant start/stop driving pattern of a mail car is a good fit for an EV and a poor fit for ICE.