Potato question...

2 thoughts - given your location there is probably still time to get a crop, although it will also depend on the variety. The trouble is the later you plant spuds the more likely it is they will succumb to blight, and this year doesn't look likely to be a low risk one at the moment. 

The other consideration is that although the spuds may look healthy, they will have been sprayed to within an inch of their lives to control diseases and pests - there is no way of knowing whether you could be introducing something you really don't want to your plot, which is why it's usually advised to only plant certified seed potatoes (and even they're not guaranteed to be disease-free.)

Growing in a bag would solve the problem of potentially transferring diseases to your plot soil (as long as you don't tip the used compost onto next year's spud patch!) although it won't reduce the chances of catching blight, which is spread by airborne spores.

If they grow well and look healthy, they probably are healthy - there are so many potential spud diseases it's probably best to look at it that way rather than frighten yourself to death 'gurgling' the subject beforehand!