There are two possibilities but they are not (almost certainly) equally likely. For 2Ps on most LHR flights, I'd guess the odds are less than 50% unless it can be confirmed at time of booking. A number of my 1P colleagues regularly fail to clear these and it's often down to 1Ks and some 1Ps at the gate.

Some flights are easier to clear, especially a particular less popular flight from hubs where 2 or 3 flights operate daily.

I was recently waitlisted on a domestic 777 segment that was showing C 50% open on the seat map up until several days before. All of those seats got assigned and my upgrade finally cleared about 24 hours prior to departure. C went out completely full and they didn't clear any gate upgrades. So it goes to show that UA is selling C seats. Good for them.

Charles