The death brings the total number of dead on Southwark's roads to three in three weeks.
The cyclist killed on Tuesday was hit and caught up in the wheels of the truck as they both turned left from Druid St on to Tower Bridge Road at around 9.30am.
Barry Mason, chair of Southwark Cyclists, has called for all skip lorries like this to be forced to have mesh side-guards over the wheels.
Barry said: "This is more tragic news. Yet again it's another skip lorry. Side-guards save lives and they only cost around £100 a pair."