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Brute force didn't work so I clearly need some kind of tool that screws into the outer thread and then into the inner thread to pull the crank off. Would that be the Park Tool CCP-44, and if so is there a budget alternative?
Thanks.
I think I've answered my own question but it'd be nice to have confirmation.
Namely that any ISIS crank puller will do, e.g. http://www.chainreactioncycles.com/x-tools-crank-extractor/rp-prod10181
Have the cranks got Raceface's "normal" 24mm GXP spindle? I could well be missing something here, but I think that the end of that tool -
(like this)
[img] 
[/img]
will disappear inside the hole in that spindle, and won't work unless you have something to bung in there that's just the right size to cover the end of the spindle. (I have a small coach-bolt that happens to have a head the right size. Washers aren't strong enough.)
If buying a new one, it might be worth getting one with a big end, which I assume is intended to overcome that problem.
Like this:
[img] 
[/img]
e.g.
http://www.chainreactioncycles.com/bbb-powerpull-crank-extractor-btl14/rp-prod4939
or http://www.chainreactioncycles.com/park-tool-compact-crank-wrench-and-puller-cwp7/rp-prod38068
Like I say, I might be missing something and stand ready to be educated.
Thanks. Good point. I already have one that pokes straight through so I don't want another!
For the record, I bought this http://www.wiggle.co.uk/lifeline-performance-2-in-1-crank-remover/?sku=5360540786 and it worked just fine. As usual, it's easy peasy with the right tools.