Slots and EATs are different things though, so I would expect them to be different. If all LHR inbounds are getting slots, its to make sure that they all don't appear at once. However 20 minutes delay can be expected as 'no delay' so the EAT is quite possibly departure time(slot time) + flying time + 20 minutes. If your a/c is on the ground at EGKB (guessing from your name!!) then TC would prefer to keep it on the ground and soak up delay there, rather than going in circles at BIG for 20 mins. This means your a/c departs BIG and goes straight into LHR without holding as the delay has been used on the ground, this makes it easier for TC as if the a/c had got airboune, it would be holding at min stack and all those before it need vectoring away before descending through it.
This only works for airfields close to the destination where the slot is issued due to the final sectors of the flight being busy (ie. holding occurring), I know it has been used occasionally from Manston into Stansted.