Vegetable Patch & Nettles

I am trying to prepare a section of garden that has not been touched for close to twenty years apparently and therefore was covered in brambles and 6ft high nettles.
My wife wants a vegetable patch in this part of the garden so this weekend with the children we have tried to clear some of it. We have been clearing piles of vegetation and roots which have mostly been burnt, but there is still a lot of work left!
One fantastic thing, as you can see from the attached picture is we discovered a stone path (theres actually another buried next to it) which was laid many years ago for a vegetable patch. It was and partly still is buried below around 5" of soil.
My question is, as we are now starting to dig over a patch and remove nettle roots, is there anymore we should do? My wife is talking about planting potatoes soon. Is the best thing to get out as much as we can see, plant it and then deal with any more that pop up, or should it be left longer?

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Get out as much root as you can, prepare the soil and plant your potatoes. There will be baby nettles (and other things!), the soil will be full of seed, and the odd one from bits of root you missed. Deal with these as you see them. Potatoes have a reputation as a good 'cleaning' crop, but this is a con: it is the hard work earthing up and the cultivation that you do growing them that has the effect
Maybe cover the ground with plating membrane, cut holes and plant the potatoes through the holes. Less weeds, but the spuds will still grow.
You can then work on other parts over the summer.
I agree with all the above
and while you're waging war on the nettles there's a silver lining to the cloud ... nettles actually grow best where the soil has a high level of nitrogen and phosphates, so it would appear that your veg patch has good soil ready and waiting for your potatoes 
Let us know how you get on - photo updates would be great
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
I planted spuds to come up through a membrane years ago. You could see the movement of all the little rodents running around under there
In the sticks near Peterborough
the rodents will be there, membrane or not though.
ideally you should put black poly sheeting down which will kill everything over time but you would have to wait a whole season to get results.
If you don't want to wait just plant out but you will have to keep on the ball with the little nettle growths which will come through.
You could also make a liquid compost/tea out of comfry or nettles when they are available which will also enrich your soil throughout the growing season.
I have grown potatoes under black plastic very successfully. Prep the soil then lay the plastic down burying the edges. Just cut holes at the right spacing then plant the seed potatoes in these. I grew Sarpo Axona and the crop was larger than those grown in bags. Some weeds were still there when the plastic was removed but they were very sad and very unhappy.
Ian, can you post a link to any "double blind" experiments which demonstrate the actual benefit of double digging please.