My understanding is any fast track immigration from Australia and into the UK is based on class of travel (except if you're on an EU/EEA passport into the UK, you can't use the fast track, why not is beyond me), but whether EY offers that I don't know.
If a frequent visitor to the UK, get signed up to IRIS. I did - and it means effortless travel from aircraft to baggage belt. The reasoning for no Fast Track line inbound at LHR if a UK/EU passport is because of the belief is that passport processing for those passports is generally quick vs non-EU ones. That has changed a lot in recent years though!
there appears to be immigration checks out of T3 these days, (it was there when I flew out in oct, but my family flew out the day before and they didn't have any immigration checks, so I don't know if this was a one-off or is permanent), but there was no fast track queue. If this is permanent, then I find it a bit odd, as there wasn't any out of T5 when I went out in december.You can use the fast track security though.
I have had my passport checked once out of two trips through T3 in the last few months. I believe it is random and based on where flights are going to. Border Security staff also stand at the gate for some ex-LHR flights and check random passports as well (I saw this heading to IST recently in T5).
I'm heading back to T3 on Wed, so will have a better look at how it's set up now. Certainly looking forward to visiting T3 Galleries F.