It's been several years, but I remember being quoted a five week wait for a custom jacket and it arrived at my door in about four and a half weeks. I'd ask them directly if you are curious, because they know better than anyone else how busy they are.
I've also heard their off-the-rack stuff gets shipped out pretty quickly, so it depends on what you're looking for.
The actual shipping/transit time from the UK to the US was pretty short, I think about three days, but out to California would probably add an extra couple days.