This lovely porcelain Cup and Saucer is in the "Old English Gadroon" shape shown in the book "Machin Porcelains & Earthenwares" by Bill Thom & Philip Miller. The pattern number is listed as 722, and is shown on page 135 of the Machin book.
The shape is also identified as Machin in "A Compendium of British Cups" by Berthoud on page 122, plate 730. He describes the cup as "having a gadrooned border under the sharply everted lip".
Both cup and saucer are in excellent condition, with no chips, no cracks, no crazing, and no repairs. Both pieces ring when tapped. The set dates c. 1825. Machin porcelains are almost never marked, but will sometimes sport a pattern number. This set has no marks or numbers. Joseph Machin worked in Burslem, Staffordshire between 1818 and 1831.
The cup is 2-1/8" (5.4 cm) high, the deep saucer is 5-3/4" (14.6 cm)in diameter.