From: "Genealogies of Connecticut Families" (1983) by Gary Boyd Roberts:

THOMPSON FAMILY:
The New Haven family of Thompson was founded by three brothers, William, Anthony, and John. An attempt has been made to connect them with the Thompson family of Lenham, co. Kent, England. This Lenham myth has been set forth as a certainty in the History of Goshen (by A. G. Hibbard, 1897), in the Marks-Platt Ancestry (by E. J. Lines, 1902, pp. 46-50), and in several other accounts, and so far as known has never been refuted.

Henry Thompson of Royton in Lenham married Dorothy Honywood, and died 20 Oct. 1648, leaving, with other issue, sons John, William, and Anthony. The coincidence of names would seem promising, and it is not strange that somebody hastily conjectured their identity with the emigrants, but investigation overthrows the theory.

According to William Berry's Pedigrees of the Families in the Co of Kent (published in 1830, pp. 15-17), Anthony Thompson of Lenham was baptized 30 Aug. 1612, and died in England 13 Feb. 1682, leaving as heiress an only daughter.

Moreover, John Thompson of Lenham was born in 1604, too early for John of New Haven, who was probably the youngest of the emigrant brothers.

The Lenham brothers had three cousins, sons of Thomas Thompson of Pethem, co. Kent, likewise named John, William, and Anthony; but this John was a knight, and died in 1645 without issue. Furthermore, the evidence of chronology tends to show that the emigrants could not descend from Henry of Lenham or Thomas of Pethem in the following generation. At all events, the accepted pedigree must be abandoned.

1. ? Thompson