Catch crops between spud rows

Radish and Rocket are both quick to grow of course, but not really an option for those who use the soil between the rows to earth up their spuds.

Think I will just mulch between my rows with cardboard, shredded paper, grass cuttings or... Something!

I had quite a few weeds pop up between my rows last year so I will put some thing down this year.  The only danger would be slugs, I suppose.

The general idea is to use potatoes to clean the land. Weeds germinate between the rows and then you come along and earth up, thus destroying them. Moving the soil stimulates more weed seeds to germinate and then you come along and earth up some more, thus destroying them. And so it goes on until the haulms are grown up and join across the rows and no more weeds grow.

Once weed seeds have germinated they cannot grow again. It is a matter of getting them to do so when you can easily destroy them.
Back on topic, I can remember seeing people plant brassicas between the rows as the haulms start to die off. I think they were cauliflowers, but I am not sure.

You only earth up a few times,

You can earth up as many times as you want. I tend to do it little and often, maybe 5 or 6 times. I find it quite therapeutic destroying those weeds as Salmo says. I keep doing it until I can't get between the rows because of the haulms.  At that point they are doing the job of keeping the weeds down.

Hmmm I have already fully earthed up by a good foot

only a little foliage at the mo but was thinking of something quick like radishes that I can pick by the time they get shaded