Is it still ( I believe it was) possible to purchase access to the LHR clubhouse irrespective of fare-code/cabin of travel?
In the past it has been possible for PE passengers (not sure about Y) to pay to enter, subject to there being space.
However given that the Clubhouse is now used for all Delta's flights, and that part of it is currently closed for renovations, I'm not sure whether that's still the case.
All you can do is ask at reception.