FWIW, My SA at Burberry has told me that alterations are included in the cost of the coat so if worst came to worst, I would think you could always have it altered to fit you perfectly even if it wasn't a P. Good luck! I hope you find it.
I bought my at Nordstrom during the anniversary sale. It has the removeable liner, and I found that it ran true to size or slightly big compared to the one that I tried on at the Burberry store in regular! Isn't that strange?!