King Edwards are main crop potatoes so have a long growing period and are best harvested in late summer, unless they become blighted, in which case cut off the foliage and remove it, and dig the potatoes a few days later to avoid the tubers becoming infected.
If you want some small tubers to enjoy before the crop is mature, dig a halum to see if they are of a usable size. I suspect they won't be much good before the end of next month as they are main crop.

Hi Veggiejo and welcome to GoY.
My answer to this is to dig around the base of a plant (with you fingers!) and feel if they are of any usable size. As Bertie says King Edwards are a "main crop" potato (and one of the best if you want my opinion) and won't be full size until September time here in the UK.

Thank you. I've found it quite confusing what with earlies, seconds, main crop etc. This is my first go at growing anything really, and everything is looking very healthy. Will have lots more questions - but glad I found this site!

You're very welcome Jo!

As useful rule of thumb is it takes 12 - 13 weeks before early potatoes are ready to harvest and 17 weeks for main crop. You can always lift a few sooner, say 14 weeks + if you are willing to accept smaller potatoes.

Choose some early varieties next year, Veggiejo, as I think you'll find it's those first early potatoes which are the tastiest, and you will get them while they are still expensive in the shops. I'm not sure of the best varieties in the UK any more as we've been in France for seven years, but here the varieties Nicola and Charlotte are very good, which may be the same names in the UK.