Its unlikely both Elements have gone O/C, but when checking them for continuity, its always worth disconnecting them first to prevent ambiguous readings, back through the Circuit.
Another thing that can be confusing when live fault finding on many Appliances is they often switch the Neutral not the Live, not sure if this one does.
But its worth remembering, as this can also lead one down the wrong path.
And one final comment, sorry to mention Elf & Safety,
but cheap test meters are ok, to a point but, but when live fault finding with "mickey mouse", cheap Test leads
, be very careful, ok for low power, but when its 240 volt 32 Amp supply, use good ones, in theory they should really comply with the GS38 standard .
Personally I am not a great fan of fused Test leads, but always use high quality ones .
Ken, G6HZG.