Convoluted but especially since you aren't stopping over I don't see a problem - apart from your taxes bill! Just tell the ICC to book segment by segment as your opening gambit, something like "I'm going to do a route from the UK to New Zealand and I'd like to specify it segment by segment" then launch into it. This could take them a while to work out the taxes though . Most likely after going through all these parts the agent will just want you off the phone so I don't think there would be a problem... you might have to ring back.

One other thing for you: Have you looked for Swiss availability for your dates - they also fly into/out of BHX & LHR, onto IST/BKK and tend to have good availability - if you want me to check on expertflyer just let me know your dates in a pm, or post here and I'm sure someone else on the board can help - it might make your return journey a BKK-ZRH-BHX for example. I also really like Swiss flights