Saxon was made at Homer Laughlin in the 1960s. There were at least three patterns used on Saxon for Cunningham & Pickett: Regal, Goldcrest, and Sunglow. Some pieces were marked with an overglaze stamp with the pattern name and "Alliance China Company" in gold. Cunningham & Pickett would resell the dinnerware to supermarkets to use as giveaways and promotions.
The Saxon name most likely comes from the French-Saxon China Company of Sebring, Ohio. In fact, the Regal pattern was first used by French-Saxon. It was commonly called "Heather" in some vintage advertisements like the one on the right (though with different hollowware for the general trade).
French-Saxon closed for a brief period after its owner died in 1963. According to The Evening Review, East Liverpool, Ohio, on March 7, 1964, it was announced the French-Saxon plant was acquired by Royal China.
By 1964, HLC was already producing many patterns for Cunningham & Pickett so It is reasonable to conclude HLC got the contract to make Regal.
While there is a strong connection between French-Saxon, Cunningham & Pickett, and Homer Laughlin with respect to Regal, the same may not be true about Goldcrest and Sunglow. Company records indicate those two patterns were offered in the mid-1960s after French-Saxon was sold.