I did this B2B yesterday 16th November on the 866, as mentioned it was a doddle arrived at gate B6, down the stairs & explained to transfer agents what I was doing, popped my roller bag and carry on through the scanner. I was back upstairs before the plane had finished off-loading.
Whole thing took 5 minutes, very easy. Could have gone to the lounge but got in line so I could get my bag above my seat as there were masses of large roller bags etc everywhere.
All in all a successful trip LHR-BUD-HEL-LHR-DFW-HNL-DFW-LHR-BUD-LHR no issues on any flights, great BA crews, totally miserable AA crews on the DFW-HNL-DFW.
Got into the Flagship First dining room at DFW and that was a lovely quiet oasis on the return.