I will be arriving in T3 on AA46 and connecting to a BA intra-europe flight out of T5. I've done this several times before but only when I had CCR access. On those occasions I followed the very helpful guide provided by CWS to walk through the tunnels. This time I have no BA lounge access. So, I'm wondering, when I arrive in T3 is it possible to get back airside to access the AA Admiral's Club (of which I am a member)? Or will I only be allowed to pass security in T5.

My Heathrow "personal flight connection plan" tells me to take a bus??