In Martin Chuzzlewit, I believe it's Mrs. Gamp who is exceedingly fond of "cowcumbers." I always assumed from context that Dickens used that pronunciation to indicate a lack of education.

I first saw this spelling in Burton’s Anatomy of Melancholy: ‘Among herbs to be eaten, I find gourds, cowcumbers, coleworts, melons, disallowed, but especially cabbage. It causeth troublesome dreams, and sends up black vapours to the brain.’

"Arise Tom Newburne" was what stumped me. Zero Googles.

I bet those particular cowcumbers that Mr. Newburne died of were in fact spoiled. As for the pronunciation shift, my guess is that the "cow" pronunciation is a product of the Great Vowel Shift of [u] to [au], and the "kyoo" pronunciation was the result of restoring the Latinate spelling.

Folk names for plants can hang on a lot longer than you'd think. JRRT uses "nasturtians" in The Fellowship of the Ring;see this page for details including an excerpt from Tolkien's letter defending it.

Here's the passage, from "A Long-Expected Party":

Inside Bag End, Bilbo and Gandalf were sitting at the open window of a small room looking out west on to the garden. The late afternoon was bright and peaceful. The flowers glowed red and golden: snap-dragons and sun-flowers, and nasturtians trailing all over the turf walls and peeping in at the round windows.

Hmm... I read an article some time ago, and googlable details escape me, but apparently in the 17th-18th centuries, dyspepsia was considered an often-fatal disease. It was usually treated with leeching, cupping, and bleeding, strong emetics, doses of mercury or arsenic, and laudanum.

Needless to say, not every sufferer survived the cure. It was a great medical mystery how a simple case of gas could so quickly become life-threatening despite rapid and aggressive treatment. I've no idea if that's what did in Mr. Newburne.

Gourds: [Supposition] They lie on the ground growing, open to human induced feces of farmyard and potty, along with wild animal or bird quano. Nature be what it is, will under the good growing laboratory conditions, will occasionaly create a way for the eater of said gourd to be eliminated, so cleanliness is required to wash thy gherkin, cowcumber, Marrow, melon, or any fruit as not every human has the correct processing system to remove dangerous poisonous substances.
Pototoe, how many people eat the flower, leaves or eyes of said spud, and how many of those that ate, stayed around to have more french fries. How many know it be a good way to remove your unloving partner.
Strangely the Tater leaf is not boiled, to make a nice cuppa or a broth, yet how many know the reason why.
Not all foods be good for all, there is always exceptions, take the lowly peanut, now removed from the freebie list of flying time fillers.
If thy be feeling funny, an [approx] hour after thy ate, check out reason why. Some results be obvious, the rejection tells you why but the minor upsets be more suttle.

How about the following for a specious etymology? -- OE. cu, cow; with OE. cumbor (cumbol), sign, standard, banner. Rather a shame it’s wrong, don’t you think?

Even so, the shift from ‘cu’ to ‘cow’ is well accounted for by OE cu. The Latinate reanalysis crew restored the ‘cu’, but it was subsequently pronounced [kju] in accordance with the ME sound shifts. That’s my hypothesis.

The Latinate reanalysis crew restored the ‘cu’

I guess it seems odd to me that such a homely word could be affected by the Latinate reanalysis crew. But so it seems to have been.

In the 1979 Polanski film Tess (as in "of the D'Urbevilles"), I recall a rustic type remarking to the title character something like "Life i'n't a cowcumber frame" which I took to mean, approximately, "life isn't a hothouse". It stuck in my mind because I hadn't heard "cowcumber" before. I had taken it for a regionalism.

Oddly, I noticed the "cowcumbers" a few days ago too. The sentence is a masterpiece in itself, although I have no idea why "forarse" should be rendered as "arise." Cucumbers can be bitter, especially at the ends, and, after all, they are tropical plants, exotic to the temperate climes.

"Forarse" was the reading of the older (out-of-copyright) edition the website is based on; the newer Latham edition has "Arise," presumably based on closer attention to Pepys' MS.