Hi, I'm flying JFK to TXL via LHR. First flight is AA into Terminal 3, and ongoing is BA from Terminal 5. I have a four hour layover at Heathrow. If I buy an Admiral's Club one-day pass to use in JFK, will I be able to access the AC in London? I mean, will I have to go through immigration or have to go around in circles to get to it?

Thanks