Double Negative

When I study English, my friend asks me malicious questions.
Hey, how do you say in English, 行かないわけにはいかない in Japanese? 
It means roughly like this, I've not admitted not going. In short, it means that I have to go. I think that we sometimes use double negative ways of speaking like this in Japanese. I use it when I want to speak euphemistically because I don't do it readily or don't agree completely. Another example is, お金が無いわけではない, it means that I don't have any money. Umm, it is difficult to translate the nuance. In short, I have money, including the feeling 'but I don't want to use it'. 
Do you also use the double negative way of speaking in English?
How do you say 'I have to go' in the double negative way?