I think you are being rather naive expecting one controller to only be dedicated to a relatively small bit of airspace. You have to remember that it is also the function of Thames Radar to control the aircraft inbound and outbound from both Biggin Hill and Southend.
Indeed and the Thames AOR is massive now but as a result of this, there is the ability to split the sector with Heathrow SVFR (125.625) and City Radar (although as City Airport was closed it is understandable that this sector was not open). Thames Radar and Heathrow SVFR were not split at the time in question. I wonder if the position had been rostered to be split or there was a shortage? In the past the shortage of staff and closure of Heathrow SVFR used to be NOTAMed.