I was in the same situation; my DH and I had a sexless marriage for seven years. He is so very lovely and we were so well-suited in other ways that it just seemed so silly to break up over it. Yet in the end the intimacy and close communication of having loving sex with your partner is such an important, human thing to want and need.
DH simply had no libido and didn't fancy me or anyone else. He was loving and kind and such a decent person.
We ended up having an open relationship for a couple of years but it was a bit of a nightmare. Although I met a nice man, to be honest 'sex for the sake of sex' is really not the same as loving sex in a committed relationship (for me anyway) so ultimately it wasn't really satisfying and DH missed the time we could have been spending together.
However I simply could not live in a sexless marriage and eventually I decided it would be better for it to end as we were fundamentally incompatible and I wanted to be free to find a relationship that included a sexual element as well as long-term commitment (I haven't found this yet but I do feel better about being available to meet the right person should they come along). Going without sex and physical love is quite soul-destroying. I know it feels selfish to think 'I want sex', but actually it is really IMPORTANT and human. You have got to address the issue.
Have you considered counselling? You can specifically get sex therapy, but I would recommend having some general relationship counselling first to address the overall situation and think about whether sex therapy would help your situation.
Open relationships do work for some people, although they didn't for us, and at least this is an honest way of addressing the issue. Would your wife consider allowing you to sleep with other people, with certain rules about how this would be managed? Should this work well for you (and I would say that absolute honesty and trust is ESSENTIAL or it isn't worth even considering) it can be a solution of sorts.
My biggest question for you is - what does your wife want from the relationship? Where does she see it going? I'm curious, because she's admitted that she doesn't fancy you, so it sounds like you've had some discussion.