Being about 5 miles from Heathow, I'm in a very dense traffic area and have ample opportunity to watch the real-time data and monitor the London TMA and Heathrow Director frequencies, and I can say without any doubt there is no delay, certainly not a 2 minute delay. Levels for the hold, heading for leaving the hold, vectors onto final approach and distance to run as passed by ATC are all 100% real-time.
Even when controlling. you are aware that what you are seeing is 'history' and you make an allowance for this. A typical example is recovering 'no compass no giro' aircraft that depend on you for starting and stopping the turns. The skill is in the anticipation of those turns and if you wait to see the effect before stopping the turn, you are already too late.
I suspect that this is the 'delay' that you think you are seeing :-)
"Adopt the no compass no giro procedure, make all turns rate one, stop and start your turns on the executive word now, is this a practice?"
Ahh! it seems like only yesterday!