The leaf growth looks like green fennel, but I'm flummoxed by the red base!

Yes it does look like fennel. Maybe the red stem is just a reaction to the cold? Report back in a few weeks!

could it be the bronze fennel, maybe that's a different colour when very young.

I thought Fennel 'Purpureum' which should grow red all over.

No - the leaves are distinctly brownish, not red, in the Purpureum variety

I have seen some forms of Giant Fennel (Ferula communis) with these reddish lugules (expanded leaf bases).

....and judging by the size next to the head of that walking stick, I would say that this is most likely what it is.

This one is rosy-pink but I have seen reddish ones too.

http://www.horizonherbs.com/images/products/Giant_anise_fennel.jpg

Found one!

http://farm5.static.flickr.com/4048/4370333983_5d98085ff0.jpg