Strictly within the question as framed, using United miles to book one-way travel on british midland itineraries. But looking at the whole picture, flying through the UK is daunting, deleterious, as in "deal killer" when t&f are considered. Freebies become just somewhat discounted. It wasn't always this way, but it grows worse and worse, so "free" travel on bmi costs more and more. I avoid Heathrow like the plague for this reason.
Otherwise, flying bmi on UA miles.....
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