I think your best bet is to check with the airlines as far as dimensions of the parts/luggage. Obviously there is certain weight restrictions. From my travel experiences, I have seen some weird containers and boxes pop up via the baggage claims. If they allow that, along with stout golf club and ski carriers, I'm sure you might be able to get way with some things, just as long as it doesnt way a metric ton or obnoxious in shape.
Btw, do you know where in London you're planning on staying in relations to where you plan on 'shopping' for parts? I only ask, because I thought about it as well, but when I mapped via google some of these places in the UK, they were 4 hours outside of London. There was no convincing my nonrover buddy how great of an idea that was.
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"Your Defender insists upon itself" Dave Parker