I’m afraid that the lack of response to your message is most likely due to a lack of ideas on how to handle this situation. I’m going to throw out some ideas for you but as usual, you shouldn’t consider the words of a forumite to be anything more than hearsay and proselytizing.
I find it unlikely that Taiwanese authorities will accept an NVQ 3 as equivalent to a Bachelor’s degree when handing out a work permit. Aside from a general unwillingness of officials to deviate from what they perceive as the letter of the law, it’s worth noting that it doesn’t matter what your degree is in, as long as you have one. In other words, experience and background count for very little and all that matters is that silly piece of paper.
Something else worth considering is that foreigners aren’t allowed to teach kindergarten; your partner’s experience likely won’t be useful when convincing immigration authorities of her credentials.
Have you considered other ways to get your “partner” out here? Marriage is one way of sponsoring her, but your use of the word partner indicates to me that you are not married and may be a lesbian couple. In the past, Taiwan has accepted joining family residence applications for gay partners who were legally married in the home country, but this may no longer be the case. Also, I don’t know if UK civil partnerships are fundamentally equivalent to marriages in UK law (and hence in the eyes of Taiwanese immigration officers).
How long are you planning on staying in Taiwan? If you’re interested in coming here for the long haul, your partner could go to school here. Aside from studying Chinese (which is one route to a student ARC), she could go the whole hog and study for a university degree. It takes a year longer than a UK degree (four years instead of three) but there are a LOT of scholarships for foreign students and she could take on private classes while she studies (as long as she’s careful about it) to supplement your income.
Another alternative would be to simply teach illegally while doing whatever she wants (studies, comes in and out of the country on a landing visa, etc). I don’t recommend it simply because it’s stressful and the consequences of being caught usually involve a large fine and deportation. Just letting you know that many people do this and it works for them.