I've just read your post in the BA forum and see that you are taking BA LHR-DXB connecting in DXB to EK for PER.

I had assumed (perhaps foolishly) that you were flying EK LHR-DXB and were enquiring about an LHR T1 to LHR T3 journey... that is a short walk underground.

DXB T1 to T3 in the middle of the night can be done on a free bus found outside the departures area. I've only taken it once, so can't comment on frequency, but the journey takes 5 minutes once moving.