You fundamentally can't. You don't have enough data. As a human, which date is involved here?
11/09/2011 10:34
Is that 11th of September or 9th of November?
If you can't tell the difference as a human, there's no chance of a computer doing so.
Now if you can get a signal from elsewhere in the same data source, then that's a start - for example, you could heuristically try to parse all the dates as US format, and all the dates as UK format, and if 100% pass as UK format but 60% fail in the US format (due to trying to days being parsed as invalid months) then you could reasonably assume they're UK dates.
That's never going to be a complete solution though - because you could have one data source with a bunch of dates which are all valid (but with different meanings) in both formats.