Ian,
You are looking for flexible metal duct. I did not realize until I looked, but it can be had in smaller sizes. Generally I think of it in the context of home made automotive exhaust systems! But a 5/8 inch i.d. tube in galvanized steel can be had from McMaster-Carr (mcmaster.com, search part number 5262k15) Can also be had in aluminum and stainless, but not in the 5/8 inch size.
A cheaper solution may by flex electrical conduit (known as BX here in the USA), though this is not fluid tight. Probably the 3/4 size is what you need.
Also for a semi-rigid but bendable alternative you may want to investigate the tubing used to connect natural and propane stoves to the gas mains. The ribs on this all metal tube are quite pronounced, so probably the least attractive solution.
You could probably scrounge a bit of the last two for free to try and see if hooking up the original carb heat system makes a difference, prior to investing in a more permanent and workmanlike tube.
Doug