I am due fertility treatment at my clinic in Denmark next week, but I won't know for definite when I need to travel until around 12–24 hours before I need to fly. I will probably need to fly out on Wednesday afternoon/evening to be there for treatment on Thursday morning and then I can be flexible as to whether I fly back on Thursday or Friday.
The flights out on Wednesday from my local airport are all sold out, and those from other UK airports are selling out fast and are too pricey for me to book now in advance in case the timing turns out not to be right.
If I turn up at my nearest airport on Wednesday what do you think the chances are of me getting on one of the sold out flights if another passenger doesn't turn up?