Any recent experience? Their website still says register on another train
I haven't heard any reports of problems (or successes) with ice axes on Eurostar this season (though I'd be interested to hear of anyone's experiences). I had no problem in March 2019, though I did hear one report last year of someone who was told (erroneously, as I understand it) that they had to send their ice axe as checked baggage.
I'm not sure which bit of the Eurostar website Peter was looking at, but there is still a clear statement that ice axes and crampons can be carried in luggage at https://www.eurostar.com/uk-en/holidays/ski-holidays (you need to scroll down to "Ski Train - what you need to know" and click the "read more" button. This appears to apply whether you are on a direct ski train, or changing at Paris or Lille - the direct ski train has the advantage that your skis don't count as one of your two pieces of baggage. I usually print out that page to wave at any officious jobsworth who queries the ice axe, though I've never had to deploy it (the piece of paper that is!).
See also my comments at https://www.eagleskiclub.org.uk/low-carbon-travel/rail-barnard (also accessible via the website menus - select Resources > Low Carbon travel and look for the link near the bottom of that page.
March 2019 I had to check in my ice axe coming back through Paris. I think it was bad luck I was scanned by a new member of staff doing the security check who decided to ask his superiors. But they just took me out to check it in and I was early enough to not be a problem, it cost £30. I wish I had had a copy of the webpage John mentioned to wave. But it wasn't too much of an issue anyway. I also got given a bit of a lecture about axes and ceremonial swords.
I like your page on train travel John. I'm also a big fan of it. I would add another tip. The TGV from Geneva to Paris is often late (at least when I get it) - so don't plan for a tight connection. Another benefit of trains though is if you miss a connection another train is usually along quite soon after and is a lot less hassle than delayed planes.
I took an ice axe on the Eurostar to get out to the Gressoney meet a couple of weeks ago without any problems - they did take my camping gas off me though :/
Thanks for your comments, Abigail - I've added a few enhancements to the train travel page incorporating your suggestions. Sorry to hear you had to pay for your ice axe in Paris last year - it does seem that not all the security staff are fully aware of the official policy, though Mostyn's and my recent experience suggest that the people at St Pancras are better informed (possibly as a result of some representations made by the BMC last year).
I'd certainly be interested to hear if anyone has problems with ice axes on Eurostar (in either direction), so we can follow it up.