We've had EE 4G available since about August last year.
There is, or when I last looked, was a page on the EE website about "EE 4G Home", but very light on the detail.
I called and asked about it. Apparently, we should be able to get this here in the next few months. "Here" being the Hampshire/Surrey border.
I wasn't left with 100% confidence that they knew what I was talking about but they did go away and "check" and there has been recent maintenance work on the tower which would supply it.
It would be nice if they offered the same "tell us your email address and we'll let you know when it launches in your area" service as was the case with the 4G rollout.