Interesting that this very recent thread is here as I am about to ask a different question on the same itinerary for January.
We are flying SJC-LHR-PRG and back, all on BA. Very familiar with Flight Connections and the purple signs. On the way in, we arrive T5, but to T3, clear security in Fast Track based on Emerald status (J to LHR, coach onward). All good.
For the return, having just experienced the First Wing at T5, we like it very much. Rather than do FCC on the return, my inclination would be to clear immigration in T3, take Hex to T5 and then use the First Wing (as Emerald).
Will we be able to make our way to Fast Track immigration in T3 (with coach PRG-LHR arrival) as a consequence of Emerald or onward J flight on BA for the immigration stop? We've done this before just by being insistent, but that was a while ago and things have changed.
Cheers.