I know nothing about electrical installations... so I’m curious. Did the op have the main switch as a 50 amp? What fuse does the Tesla charger itself need?
The issue here relates to the maximum current that can safely be drawn from the supply that comes into the house, and this varies with the age of the wiring into the house, the size of the incoming cable, plus whether or not the supply is shared with an adjacent house or house. Over the years supplies have changed, plus back in the mists of time some regional electricity boards used to do things differently to others, so, for example, 60 A incoming supplies are commonplace in some areas, whereas 100 A incoming supplies are the norm elsewhere. Lowest I've seen is a 40 A incoming supply, and the most common seem to be either 80 A or 100 A.
The supply coming into the property will have a big fuse, rated at the maximum that the supply can deliver. These fuses cannot be accessed or changed by anyone other than the local Distribution Network Operator (DNO), or sometimes the electricity supplier, and are sealed behind a plastic cover, usually just below where the meter is fitted, and right where the cable comes in.
The supply from that fuse connects directly to the meter, and then two, fairly fat, cables take power from the meter to the consumer unit (CU, also sometimes called the "fuse board"). That has a switch to isolate all the power to the house, plus protection devices for each household circuit (fuses for an older CU, Miniature Circuit Breakers, MCBs, for newer ones). There may be additional protection devices in the CU too, like Residual Current Devices (RCDs), or the individual circuits may have combined RCDs and MCBs, things called RCBOs (Residual Current Breaker with Overload protection).
Each circuit in the house will be protected, either by a fuse, MCB or RCBO, so that, in the event of an overload, that will trip/blow and hopefully prevent overheating that may cause a fire. Most high current loads in a house aren't on for long periods of time, an hour or two at most, usually. A charge point is a bit different, as it's a very high load (in domestic terms), around 7 kW. This is roughly the same as two and a half immersion heaters. Also, a charge point may be running for many hours on and - a Model 3 could take around 10 hours or so to fully charge, for example.
Because of the combination of the high power, plus the long duration, of a charge point load, and also because a charge point requires additional safety protection (because the car may be outside, has a metal body that can be touched by people with their feet on wet ground, perhaps, etc) it's best to take a separate connection from the incoming supply, before it reaches the CU, and connect that to a separate small CU, that contains the protection device(s) for the charge point, then run a fairly heavy duty cable from there to the charge point itself. A 7 kW charge point will be protected by either a 32 A or 40 A protection device normally. Fuses aren't normally fitted, as modern protection devices allow power to be restored by resetting the over-current device once a fault has been cleared.
The problem in this case is that the installer failed to do the mandatory assessment of the total load for the installation. There are ways to estimate how much power the house uses, or this can be measured over a period of time, and this, together with the 32 A that the charge point is going to draw, has to be added together and the sum of both must be less than the rating of the incoming supply. Some people are finding that, in order to have a charge point installed, they are having to have their incoming supply uprated.
If the incoming cable and local network has spare capacity, as in this case, this may be simply a case of changing the incoming fuse for one with a higher rating. If the incoming cable, or local network, has not got enough spare capacity then it can be costly to get the work done. This does seem to vary widely from region to region, though, with some DNOs charging a lot of money for local network reinforcement, and others being more relaxed about it and charging less, or even doing the work at no cost.
