Harvesting Sweet Potatoes

[Humbug carrot]

I have 3 sweet potatoes planted outside through black fabric, they started off under cloches but soon escaped and are now wandering happily through the sweet corn.
When would be the best time to harvest them? The leaves are still green and healthy looking. Would it be best to wait for the first frosts to nip the leaves, or get them out sooner?

[Humbug carrot]

[manicscousers]

Hiya, welcome to a4a   
Saddad is good with sweet potatoes, hope he comes along as I need the answer, too