"The English surname HAMPSON is of patronymic origin, and simple means 'Son of Hamon' [or Haman], with the letter "p" being intrusive as in the case of Thompson. Records from the 14th and 15th Centuries show that Hamon was a popular choice as a forename. Its diminutives - Hamelot, Hamonet and Hameline surviving into the 18th Century as a Baptismal name, Hamon having lapsed by then into oblivion.
"Records from 1379 in Yorkshire include the reference to one Robertus Hameson and in 1354 the Register of the Freeman of the City of York record Robert Hamsane. The Yorkshire Poll Tax Returns refer to a Henry Hampson in 1540."
With this evidence, the Yorkshire origin Hampson surname likely predates the Londonderry origin, although the name is much more prevalent in Lancashire than Yorkshire.