I'll start with a vocabulary note. 'Wash up' in British English means 'wash the dishes'. This is not to be confused with the American meaning of 'wash up', which means wash yourself. I'm sure that many an American guest in a British household has confused their hosts by saying 'I'll just go wash up before dinner'. Now for the grammar. In this situation, the meaning is exactly the same because the scenario is clearly explained. We understand that a helpful house guest washed the dishes by hand, not realising that there was a dishwasher. In this situation, both sentences mean, 'What you did was not necessary'. The first would be used by both AmE and BrE speakers, the second only by BrE speakers. However, there are some situations where there is a difference. Look at this sentence on its own: "I didn't need to wash the dishes." That statement, without any context, is ambiguous. It could have two meanings: Scenario One: "I didn't need to wash the dishes. I washed them all by hand, then I realised there was a dishwasher! How annoying. What a waste of time!" In this situation, 'I didn't need to' means that I DID wash the dishes (even though it was unnecessary). This is the same as the situation above. Scenario Two "I didn't need to wash the dishes. There was a dishwasher, so I just put everything in there." In this situation, 'I didn't need to' means that I DIDN'T wash the dishes (because it was unnecessary). Without context, how can we tell the difference between those two totally different meanings? Quite simply, you can't. Now, this is where the very convenient 'Needn't have' comes in useful. In BrE, we can use 'needn't have' to make it crystal clear that we are referring to the the first situation only: "You needn't have washed the dishes" This is totally clear and unambiguous. It means that you did something that was unnecessary. It can only describe the first situation. Unlike "I didn't need to wash the dishes", it cannot refer to scenario two.

Your question has been answered in the comments. Both mean the same thing, but the 'needn't' form is much more common in British English.

Thank you!

I agree they mean the same. I feel very comfortable saying 'needn't have..'. I am a British English speaker.

i think its european english or australian.