I'll admit to the amateur mistake of not handling leading white space (that's now fixed on the master branch.)
It looks like the only example from your list that couldn't be parsed is "The day before Sunday week". Forgive my ignorance, but I've never seen 'week' used in that context here in the US. If you'd be willing to describe the proper use, I'll look at implementing it.
As for the UK format, please see the issue I created here: http://github.com/joestelmach/natty/issues#issue/3, and lend some advice if you'd like.
The test set is available here: http://github.com/joestelmach/natty/blob/master/src/test/gun...