The thing is new potatoes (1st earlies as they are known) are not meant for storing, they are meant to be dug up and consumed. Main crop spuds which arrive later in the season are for storing and are best kept in either either hessian sacks or paper sacks, in a cool dry place.
For the past 4 years I have shied away from growing spuds in the ground and more or less grow all of them in containers. The main reason being they will store happily for months in the containers and compost they were grown in. They always come out of a container blemish free and no slug holes !