Earlies won't store very well - they are small and lose moisture easliy, and they'll lose some of that lovely earthy freshness. Just use them as you need them - you don't even need to pull up a whole plant at once at first, you can just feel around in the soil and pick out a few potatoes, leaving the rest to grow on. If you're keen to clear the space, I suppose you could try storing some in a bucket of soil for while, but I've never tried this.
