My investigations have revealed that both immersions are on the same 16A radial circuit. The only other thing on that radial circuit appears to be a secondary circulation pump.
Does that mean that I must not run both immersions at the same time?
And if not, can the circuit be upgraded to 32A simply? The cable is 2.5mm t&e
Edit : and also, if they each draw 12a,why didn't the cu trip when the were both on at the same time?
No, you shouldn't be using both at the same time. MCB's do not instantly trip on rating + .1amp. How quickly they trip, depends upon excess load and time it is on for. A 2.5mm cannot be fed from a 32amp MCB, but if you let us know about the length of the 2.5mm, and identify the route of the cable (buried in plaster, clipped to surface, buried in insulation), someone will be able to advise the maximum size of MCB which can be fitted.