Passport Renewal in UK

Okay I admit I am in panic mode-- I did a search and did find a couple threads but thought I would start a new one and see what everyone's recent experiences are. I am due to travel to the states for the first time in years on 31 May. I just checked my passport and of course it expires 30 May. I of course googled right away and see that you apply by post (phew- was afraid I would have to go to London!). It says 15 business days-- that gives me enough time, but not much extra.
So you all know the question that is coming-- reasurre me please with lots of postive experiences of how quick and wonderful they are!!
(Thank God I looked-- my dear parents bought my ticket so I would be there for their 50th, I would have been horrified if I didn't discover this in time!!)

Mine wasn't recent but the turn-around was very quick. 

Good luck--I hope you get it in time!