So it appears there was unforecast weather and a badly overloaded single ATCO on Approach.
Have you all filed ASR's against the Spanish authorities?Was the unit correctly staffed? As an approach controller the first thing I do (when things are becoming brisk or an unforeseen event occurs) is get someone else in beside me. The bare minimum is a second pair of eyes and someone who can co-ordinate EAT's or (usually by phone) diversions leaving me to do the basics of vectoring .To do it alone is madness.
Stopping departures may lead to ground congestion and that MIGHT impact on the (already)very low landing rate but would greatly ease the pressure on the APP controller.
I would be filing an Overload report with my management if I were him.