Catawissa and the Egyption are most common here, and were imported by the 1700's, but I think not from England, rather other parts of europe.

Just curious as to which or if any are common in britain and how long they have been documented there.

They are called "walking" onions here, usually. I couldn't say they are widely grown here either, but are definitely present among enthusiasts. They were very common in the northern US and Canada until the decline of the family homestead.

I would be hard-pressed to extol their virtues sufficiently: a fabulously well-adapted plant, tolerating fairly acid soil below 5 up into the 8's, extremely cold-hardy; a perrenial source of fresh vegetable as early spring scallions, late spring as a green onion often the size of a leek, early summer the tender top-sets are a nice edible, late summer the basal bulb can be used and by fall there are new green sprouts on thru winter; the continuous and multiple propagation is so easy that they are considered an invasive in some places.

The multiplier onion, a somewhat different animal, is common thru the middle and deep south of the US. It is not very cold-hardy. Perhaps this originated from southern england? I propose that england must have had some traditional type of onion not propagated by seed, as seed-grown onions are fairly recently developed from the spanish strain, and are fussy and labor-intensive - not for the farmsteader.