Leaving the soil as undisturbed as possible means the capillary structure remains intact and roots have better access to lower reserves of moisture.
However, plant roots also like surface moisture! so mulching with paper and cardboard helps, (cardboard is easier to handle and weight down) except that in wet summers, too much mulching with unrotted organic matter can allow slugs to proiliferate under them. Hence the use of compost, a shame you do not have any. Also keeping soil clean of weeds helps contain moisture.