I discovered the correct answer to this in the end, which is: go over them with a damp cloth with some shampoo on it. Then another damp cloth without shampoo to get the shampoo off. Not too wet. Thanks to my local shoe shop!
Following this and after letting them dry I mixed together two shades of red shoe cream (one too dark and one too light) to get just the right colour, put a liberal amount of this on, left it overnight and buffed lightly in the morning. Came up great, looking almost new.
They're not as nubucky as they were because of the shoe cream but I can live with that, they are properly red again and not grimy.