TBH then Fisher, I don't see for the life of me what you are worried about.
If your description is correct.
Yes you have 400V phase to phase rms.
You have 230V phase to earth rms.
Your flex on your kettle or toaster has 230V phase to earth, and the conductors on that are a lot more vulnerable than those in an SWA cable.
The SWA has a layer if insulation over the conductors, then a layer of polymeric bedding, which has insulating properties, but is not officially an insulator, then an earthed steel wire armour then a layer of polymer sheathing, which also has insulating properties, but again is not officially an insulator.
Plus they could have 2 earthed conductors under the bedding as well.
IF the cables have been installed correctly then working around them, water or no is fine, your electrical person on site was quite correct.
You do however, know that the cables are not damaged don't you? After all you should be maintaining the installation in accordance with EAWR, thus compliance with BS7671 should be assured, thus, your last periodic inspection (PIR/EICR) should show that the cables are fine.
The confined space bit I can't comment on as I've not seen it, not my speciality either.
Jane, I agree, that is the thing with HV stuff, the stored energy in the cables after isolation can be considerable due to the cable capacitance, many don't realise this.
It's one of the reasons the DNO's spike HV cables before jointing.
If the OP had not described the situation in the way they did then I would not have taken the route that I did with my answers.
In a lab environment, as you say, possibly very different, again in Heavy Industry, & Electrical Distribution, but in the latter two, you will have SAP's who know their stuff in charge of the HV if it's their responsibility.