In addition to Canuck's suggestion in the comment below - which is probably the most direct approach - you may also try to find this map in a library, and if you are close enough find out their policy on taking digital images with your own camera. This will vary by institution. Some may even, if you reach out to them and if their policies allow (and you get the right person on the right day and ask really nicely), be willing/able to provide you with an image.
The map is for sale on some commercial sites, including Bibliophile, which helpfully cites the source of the map as Thomas Moule’s English Counties Delineated.
WorldCat (an online catalog of the collections of many libraries) has several entries for works matching that title. This is often the case, especially for older works that were cataloged separately by many institutions prior to the cooperative system of "copy-cataloging" that is in place today. Among these I have identified three matches that are probably the Atlas in question, and which are held by public institutions in the US.
Record 1
Record 2
Record 3
Again, this is the more labor intensive approach - if the Wikipedia user who has the image gets back to you, that would certainly be easier. Or you could spend the money on a copy from an antiquarian mapseller.
You might try contacting
You might try contacting Wikipedia user "Pointillist," who claims to responsible for the digital image that's used extensively on Wikipedia (see description). It's not clear whether the various sections displayed on Wikipedia came from an image of the full map or not, but it doesn't hurt to ask.