It could be seen as an English equivalent of the French Mornay sauce[1] (itself a variant of Béchamel sauce traditionally mixed with half Gruyère and half Parmesan).
It can be purchased both as a ready to use sauce and as a powder in British supermarkets.
In the United States, a mass-produced cheddar sauce is purveyed under the Ragú brand, and is called "double cheddar sauce".
[2] Cheddar sauce can be used in a variety of ways including being poured over meats, types of pasta, vegetables and even as a dip.
[3] It is used in the preparation of a variety of British dishes, including the following: