I believe that the first Binch came to England prior to 1578 from Binch, Belgium (now known as Binche). Binch was famous for lace making, and many of the Binch men in Calverton, England were lace makers. The following is an excerpt from The Penny Cyclopedia of the Society for the Diffusion of Useful Knowledge published by C. Knight in 1843.

To learn more about the town of Binche (Binch), please see the following articles.
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I found an article about Binch, Belgium in an old copy of The Penny Cyclopedia of the Society for the Diffusion of Useful Knowledge. You can get the whole collection at Archive.org.

Binch, Belgium

Title: The Penny Cyclopedia of the Society for the Diffusion of Useful Knowledge
Publisher: C. Knight
Publication Date: 1843

BINCH. an old town in the province of Hainault in Belgium, situated on the high road from Mons to Charleroi, about ten miles east of Mons, and thirteen west of Charleroi.

Binch was built in 1110 and surrounded with walls. For a long time the Counts of Hanault were accustomed to it as a dowry with their eldest daughters. In the war between Henry II of France and Charles V 1554 it was taken by the former and burnt, but was soon after rebuilt. In 1578 it was twice taken, once by the Spanards, and afterwards by the French under the command of xxxx of Alengon. It was afterwards retaken by the Spanish and remained in their possesion until 1686, when under the treaty of Aix-la-Chapelle, it was given up to France. Ten years later this town again came under the dominion of Spain by the treaty of Nimeguen.

Binch, which is built on the summit and half way down a bill is remarkable for the picturesque spots which lie about it. The town is still surrounded by walls, and contains 760 houses, man of them of considerable elegance. One principle street traverses it from one end to the other. It contains a fine square ornamented with a fountain, a church, a college established in 1725 under the management of the Augustines, seven elementary schools, and a hospital. Previous to the burning of the town in 1554, it contained a fine castle, which was the favorite residence of Maria, Queen of Hungary, the siter of Charles V. The remains of this building at present consist of a scarp flanked by towers, which has been converted into a terrace into a terrace prominade, offering very fine views; the rest of the site of the castle is occupied by kitchen-gardens.

The town contains several manufactories. The chief branches of industry are connected with the leather trade, comprehending tanning, currying, and shoe-making, in which last 400 workmen are employed. On the 16th day of each month a fair is held for the sale of horses and cattle: there are besides three markets in each week-on Monday, Thursday, and Saturday.