I'm really sorry to have had to be a bit negative but the risks of continuing to use an installation, or even portable, LV system with no earth and no real protection from electric shock are high. Given that the inverter must have a fake CE approval (it cannot have passed with that outlet fitted, for a start) then I think it's very wise to get it tested.
If it were me (accepting that I probably feel a bit more confident about taking stuff apart to examine it than some) then I'd open up the inverter case and examine the internal construction and layout, looking for visible signs that the design pays heed to the need for adequate isolation between the ELV DC input and the LV AC output, together with adequate insulation of high voltage areas from the metal case. I'd also want to see that the earth pin on the socket was properly connected to the metal case.
Assuming all was OK internally, then using this as a temporary supply would then be OK, provided that a protective earth was provided, by means of an earth rod connected to the metal case and earth pin on the socket, together with a plug in RCD to provide protection downstream from the unit.
I really wish Trading Standards had the resources to stop all the non-compliant, and potentially dangerous, electrical stuff that is sold via Ebay and other on-line sellers. Back when I was investigating and testing LED lights to use in our build I even found some lethal GU10 lights being sold by one of the very well-known DIY stores. To their credit they did withdraw them from sale immediately when presented with the evidence (the LEDs used a capacitive dropper, so weren't isolated from the mains supply, and had bare chips on the front face, with a 50:50 chance that they would be at line potential..............). In this case the seller is clearly in China, selling via a drop-shipping arrangement in the UK, and using a UK address as a mail box. Trading Standards could do nothing more than close down his present seller ID, I think, and I'm certain the seller would just pop-up again within a day or two with a new ID. My experience is that Trading Standard just don't bother chasing things like this, as they know they are wasting their time.