From clear as mud to clear as crystal. Thanks to all.
Well yes and no.
It is perfectly legally satisfactory to use the Gross Train Mass Minus the Gross Vehicle Mass calculation to indicate the MTPLM of the trailer you can use, It will always give a legal weight result.
But being more pedantic the calculation of GTM - GVM actually tells you the maximum permitted weight on the trailers axle when the tow vehicle is fully loaded. Some tow vehicles (not all) are rated by their manufacturer to be legally able to tow heavier trailers ( the tow vehicles maximum Towed Trailer Mass in the vehicles specifications), by virtue of every kg the tow vehicle is under its GVM limit can be transferred to the trailers (provided the trailers individual limits are not exceeded.)
Also the towed weight limit does not include the nose load which for technical reasons is not "towed" but carried by the tow vehicle. This can also give some outfits the opportunity to have a trailer whoes MTPLM exceeds the GTM-GVM value.
Both these situations have to be set up very carefully to take advantage of the extra trialer weight involved, so unless your desperate to eek out the greatest possible towing capacity, they're best forgotten.