Any other dates will likely be in the same order as written. For instance, the rhyme for bonfire night is 'remember remember, the fifth of November'. I believe that many in the US also talk about the fourth of July, rather than July fourth, so it's not like English has the hard-and-fast rule you were proposing.
Technically, I'd drop the "th of" and just say/write "11 September 2001".
It took me a while to figure this out because actually it's quite rare to speak a date including a year without reading it - most spontaneously-spoken dates are this year (so the year is implied) and for a read dates, I'd probably say whatever was written.
The clincher was how I'd say my birth date, which would be of the form above.
I'm not claiming to be the definitive British English speaker, though! ;)
...and as another poster commented, it might depend on context - for example, "September 11" is often used in British English because it refers to an American event.