I think 'moose' is becoming a bit more common - I suspect simply because it's the more familiar word to the general public (to put it bluntly, moose get a lot more mentions on American TV than British, so exposure to the word elk is pretty minimal in comparison. Indeed, as I'm typing this there is a moose on my telly that has just been called 'moose', in a slightly perturbing coincidence!). I avoid 'elk' in all English-language contexts as it's simply confusing (see previous moose/elk threads! ). 'Moose' and 'Wapiti' cover all cases without confusion, so we don't need 'elk'.
My personal view is that Americans can call their animals whatever they want and we ought to use their names for their animals too, if we have nothing better. But I'm never going to use the name duck hawk for a peregrine, neither will I say moose when I should say elk. If that confuses people I am perfectly happy to explain the difference between a moose and an elk.
A quick internet check shows that the Whipsnade website uses the m word, while the ZSL inventory says European elk. The HWP website says Eurasian elk - it's my favourite
If you ever see me near this sign with a can of spray paint in my hand, please gently restrain me
My personal view is that Americans can call their animals whatever they want and we ought to use their names for their animals too, if we have nothing better. But I'm never going to use the name duck hawk for a peregrine, neither will I say moose when I should say elk. If that confuses people I am perfectly happy to explain the difference between a moose and an elk.
If it were simply a case of Eurasian vs. North American Alces, I'd agree. The potential confusion comes because, as you know, 'elk' in the US refers to a completely different animal - and it's confusion that is completely avoidable using established names, so I do!