What's required in the way of protection depends on the type of supply. Installations that are wired with a TT earthing system, for example, don't need open PEN protection, as they don't have a PEN conductor to fail.
There are essentially two fault conditions that can occur that may require protection devices to be fitted to the supply, or have equivalent protection built-in to the charge point itself. The Tesla Wall Connector doesn't, yet, have any UK regs compliant protection built-in, so if connected to a typical UK TN-C-S/PME domestic supply it will require both open PEN protection and also DC tolerant earth leakage protection.
The open PEN protection is to protect against a fault external to the installation, where the combined protective earth and neutral (PEN) conductor coming into the premises goes open circuit. When this happens, current can flow through any devices that are switched on, causing the voltage on the neutral and protective earth (so any exposed earthed metalwork) to rise to a dangerous voltage relative to the true earth potential of the ground outside. As the car body is connected to the PE, if plugged in, it could become an electric shock risk.
To protect against this fault either an RCD and earth electrode close to the car charge point location can be fitted, or an open PEN protection device can be installed on the supply to the charge point. The earth electrode doesn't do exactly as suggested above, it's really there to provide a path to local earth for just enough current to trip the RCD. The resistance of an earth electrode is usually way too high for it to take any sort of realistic fault current without the voltage rising to an unsafe level, but the RCD will trip at less than 30 mA, a current that is considered to be below the threshold that may cause the heart to stop.
In practical terms, it's often a lot easier to fit an open PEN device now. Installing an earth electrode sufficiently far away from other services, and yet close enough to the charge point location to be effective, is often difficult, especially on houses in urban areas. The open PEN device is a bit more expensive (around £120 or so) but is quicker to fit, and allows open PEN protection to pretty much any installation.
The second fault condition that needs protection for any installation, regardless of the earthing system used, is DC tolerant earth leakage current protection. This requires a Type B or Type EV RCD to be fitted to the supply, if the charge point does not contain integral DC tolerant earth leakage protection. It's usually possible to fit a Type B RCD inside the same enclosure as an open PEN protection device, making the installation neater and easier to wire up. A Type B RCD costs around £114, so the cost of both an open PEN device and Type B RCD will be around £230 or thereabouts.