I think, but am not certain, that potatoes did not become common in England until the mid to late 18th century. The Loudon's Encyclopedia of Agriculture (1847) says that

It was near the middle of the 1700s that they were known over most of the country, and since that time they have been extensively cultivated.

However, Jeff Chapman notes that

In 1795, the Board of Agriculture issued a pamphlet entitled "Hints Respecting the Culture and Use of Potatoes"; this was followed shortly by pro-potato editorials and potato recipes in The Times. Gradually, the lower classes began to follow the lead of the upper classes.

That as late as 1795, the Board of Agriculture should need to issue a pamphlet promoting the production and consumption of potatoes, suggests that they had not yet achieved the ubiquitous status they would have by the 1840s.

So I would go with an date around 1800 as the very earliest you could expect to find potatoes as a common cash crop in England, although I think you could add or subtract 20 years from that date depending on region and class.