I've never known a home grown new potato that didn't have a thin skin you can just rub off with a vegetable brush under water. The snag with the ones in the supermarket is they been sitting around for days or even weeks. Try Maris Baird or Rocket.

The new ones only need washing well,Nimrod...unless the reason is because you don't like the skin..I would imagine they would fall apart more easily when boiled ,without,a problem sometimes with some varieties..but ok when steamed..
So many varieties on the market now,but I found Vales Emerald,and Swift to be very good..There are various 'Potato days' around the country..where you can get advice,and able to buy potato's from just one,to however many you want,in different varieties..maybe you could 'google ' it,to see if there are any in your area ? Our local one is in two weeks time..good luck..

"International Kidney", grown as an early is very good. Grown on Jersey as "Jersey Royal".

As moon growe says, with early home-grown potatoes the skin just rubs off. Pentland Javelin when steamed just melt in your mouth - no skin to speak of ... you can just push them through your teeth!