Just to be clear, installing an earth electrode isn't an automatic fix, or way to make the installation comply with the regs. It may or may not form part of the solution, but not all of it, as there is also a requirement to disconnect the live conductors (line and neutral) AND the protective earth conductor, in the even of a fault. The latter point is the gotcha, as most RCDs and RCBOs in domestic installation will only be 2 pole, so will not disconnect the PE to the outlet.
The method I've used is to use a DC tolerant residual current sensing device, coupled with a 3 pole contactor, with that being protected in terms of the required high fault current disconnect by a 2 pole Type A RCBO. The 3 pole contactor allows compliance, because in the event of a fault the sensor will disconnect the line, neutral and PE from the vehicle. The reason for needing to disconnect the PE is because of the touch voltage problem - the car body needs to be disconnected from the incoming PE if that has floated up to a high voltage because of a PEN fault.
Any outdoor circuit has to be installed by a Part P accredited electrician, with the Part P installation certificate lodged digitally on the building control accessible database, so there is no lawful option to install a new DIY outdoor circuit. That's not specific to car charging, it applies to any outdoor circuit, and has done for quite a few years now, since the introduction of Part P of the building regs. We encountered this problem when selling our last house, as I'd installed an outdoor weatherproof outlet, connected as a radial to a spare MCB in the consumer unit. The surveyor for the purchaser picked it up, and although I'm a competent person, I wasn't Part P registered, so I opted to disconnect the power outlet from the CU before sale, just to avoid the hassle it was likely to cause. I left the wiring in place, labelled, so the purchasers could get it reconnected if they wished.
By the same token, DIY of any outdoor outlet for a charge point is also unlawful, so needs to be done by a competent person that holds a current Part P accreditation (unless you live in Scotland, where they are thankfully free from all this Part P stuff). Fitting something like the matt-e device (
https://matt-e.co.uk/ ) is pretty easy, and is reputed to meet the requirements. I've never installed one, mind, but it does look to be pretty straightforward, and doesn't require installing an earth electrode. An alternative might be to replace the existing RCD with one of these, although they are a fair bit bigger:
Electric Vehicle Charging | Western Automation
EDITED TO ADD:
As an afterthought, it's fine to DIY any existing circuit, at least as far as Part P is concerned. It still needs to be done by a competent person, but as no paperwork has to be lodged anywhere for just minor changes to something that already exists that means a competent DIY'er can do the work. Should have mentioned this earlier, as it's how I wired up lots of outdoor stuff here. When we built the house I ran several spare runs of cable around, anywhere I thought we might want to connect something later. All these runs were terminated in weatherproof junction boxes, and were inspected, tested and included on the Part P chit. This meant I could legally connect things up later, without needing to get a Part P chap in again, as all I was doing was working on an "existing circuit".