mirrored glass is unlikely to comply with BS6206. Glass that does comply with BS6206 (or it's successor EN, the number of which I can never remember) must be stamped with the BS Kitemark.
If it's stuck to board then it's likely to be very thin, in order not to put too great a strain on the hinges, and the flank of the wardrobes. The key thing is how it is stuck. I've seen mirror glass stuck to walls with squidgeguns - a grid of adhesive that is compressed when the mirror is pressed against the board, but doesn't neccessarily spread over the entire board. That's clearly not as secure as putting the mirror glass against a bed of adhesive, but, even then, as the panel flexes the adhesive can de-bond.
Annealed glass is tough stuff, but, when it breaks it's nasty (BS6206 'safety' glass can cause injury when it showers down on a child, but it's not nearly as big a risk). 50% of all plastic surgery time in this country is devoted to glass injuries, most of which are domestic. A fair proportion of these are drink-related, which (one hopes) isn't too much of a concern with your kids, but, if my supposition about the construction of the panels is correct, then there is no way I'd live with them.
If it's not stuck to board, that is to say if it's a piece of glass hung from a track, then measure the thickness. I haven't got a problem with unframed glass (I might find a snap of a building with cantilevered glass balustrades, designed by yrs truly) but it has to be strong enough to do the job. The risk with glass that is strong enough to do the job (say 10mm thick) is that it is fantastically heavy, and if it falls on you it's a serious thing. The risk with glass that isn't strong enough to do the job is that it might break. Either way there are better places to put it than a kid's bedroom.
It is just possible, although pretty darn unlikely, that the glass is laminated. It would probably be either 6.4mm or 8.8mm. That would be safe enough. You would see the edge of the polyvinylbutyral (PVB) interlayer at the edge of the glass - like a thin layer of transparent marmite in a sandwich
As an aside...
Part P of the Building Regulations governs electrical safety, costs £250million a year and probably saves 5 lives a year. Part N of the building regulations governing glass in windows (but not in furniture) could be uprated at a far lower cost and save many times the number of lives, let alone injuries which include scarring. It's not going to happen anytime soon. I've tried and failed, but the annealed glass industy retains a great deal of clout.
