You could be on the tail end of a looped supply, I remember reading/watching something about these issues, it was common in the 70's to feed a semi detatched block of two houses from the street main in to one side of the house block then run from there to the other side of the house block. the likelyhood of both houses using high current devices (showers and cookers) at the same time was minimal and the feed in from the street main was sized accordingly, now when these houses decide to fit car chargers, that will both be on overnight in most cases, the cumulative current exceeds the feed in rating by some margin and over a longer time period thus things start to get warm.Interesting that, just checked my 2nd property which is a 2000 converted barn, terrace arrangement. Non looped but with only a 60a fuse. My main concern would be my parking is out the front and my electricity stuff at the back...
In these situations both houses would need their feeding arrangements changing, giving an individual feed in from the street main sized accordingly to account for the increased load.
This of course is only realised once the car is at home and the electricians coming to install the charge point says 'Nope! Can't do it' and the DNO says 'We'll be able to do the ned feed in's to both properties in 6 months time, IF the neighbour is in agreement.'