Nick,
I started when I was 40; I'm 55 now. I worked very hard, practicing 2-4 hours per day consistently. I also had a decent musical background from playing classical guitar and singing Renaissance and Baroque music in small groups; I already had basic music theory under control. I had a couple of good teachers, and a few useless ones. At this point, I've got an excellent teacher, a retired, mid-tier concert pianist and music professor who likes teaching adults and is good at teaching technique. I did a decent job playing the Haydn Sonata Hob 32 in B minor at a recital recently. The stuff I've played competently (meaning you wouldn't necessarily pay to hear it, but you wouldn't run out of the room screaming either) includes most of the Schubert Impromptus, the Brahms Intermezzi in Opus 117 and 118, Beethoven Sonata Opus 14 #1 in E major, Opus 10 #1 in C minor and the Pastorale Sonata (just starting it), Bach P&F from WTC Book 1 in C minor, D minor, D major, A flat major, and Gmajor, French Suites in E flat and C minor, the First Partita, a few Mozart sonatas including the wonderful A minor sonata, lots of Haydn sonatas, an easy Chopin Nocturne in G minor, Janacek's "On an Overgrown Path."
You have to work harder than someone who started young and you have to find a teacher who will teach technique and who has experience teaching adults. Other than than there's absolutely no reason not to go for it.
Bill