Using the current routes and method of navigation there is inherently a degree of uncertainty about the accuracy in the way they MIGHT be flown. It is not possible to reduce the time interval between departures because ATC would sometimes have to intervene in a random number of cases to maintain separation.
The whole point of the new routes and how they are flown using PBN capability would mean the time interval between aircraft taking off from Heathrow could be reduced in some circumstances without ATC intervention being needed to provide separation. The greater accuracy and certainty of an aircraft being able to fly any particular route is where the increased resilience in Heathrow airport operations would come from.