I have heavy clay here in NW London and the first few years I dug out potatoes like you. This year, year 3 of no-digging, I popped each tuber in a hole dug with a trowel, then mulched from July with comfrey cuts (I have around 20 plants, some more vigorous than others), plenty so tubers pushing up were not exposed to light.
When I harvested, I pulled the plants out by hand and then harvested tubers using my hands. Although the odd one took a bit of removing, 95%+ just came out easily. We did have a lot of rain from mid July which may have helped. I harvested Desiree late August and Sarpo Mira at the equinox.
The yields were 2.5 – 3lb per tuber, spaced in a 40cm*40cm grid, which was around 20lb per square metre. Almost no disease, maybe 5 of 300 good sized tubers had minor slug damage. No scab at all this year.