Having tried growing potatoes in the ground the first year I had the allotment, I came to the conclusion by year two that the combination of rain and blight means that this is a crop that is more sensibly grown in potato bags or a container.
Fill a potato bag or container with some of the chippings you have had rolled up in a carpet for the last 12 months, to about 1/3rd its capacity, and then drop some potatoes that have started chitting (throwing out shoots) on top of it. Add another third and repeat the exercise then fill the bag to near the top.
Within a few weeks the potatoes will have reached the surface and withing about 6 to 8 weeks they will have flowered and started to fruit. Keep children away from the fruit, they may be the same family as tomato and look like tomato but the fruit on the potato is poisonous.
Once the plants start to fruit they should be ready for taking out of the bag and you should have a nice supply of new potatoes. If you plant fresh every 3 weeks you should have a good supply of new potatoes throughout the summer and autumn.