Yes, England and Wales has something like it, but NIED wouldn't be what we call it. I'm not happy with some of the POV titles in the wikipedia law (which is mostly US law with notes), which is why I am reluctant to contribute further to articles like Tort. Essentially they mislead more than they inform by trying to set out one jurisdiction (the US) but with suitable weasel words to try to make it more universal. The result informs no-one properly. 

For the record, we have specific rules about psychiatric injury, but also permit recovery for emotional distress in narrower circumstances under the tort of negligence.