LHR Showers
While it's not the same terminal as the EWR arrivals, I did use the showers in the Star Alliance lounge in LHR when coming in from LAX. I had asked the purser on-board what I needed for access, and he said typically I need to be invited...and the CSA greeting the plane would assist with that. Of course, the CSA disappeared on landing and I went to the lounge ...and they needed nothing other than my boarding pass + passport.
With the showers, there's nothing to sign up...you just go, pick one, use it, and exit. I found the LHR bathroom/shower set-up to be nice; great rainhead shower with perfect warm/hot water.