They enjoyed a solid first third of the season but have been inconsistent since, and were beaten 4-1 by Whitby Town at the weekend.
Chairman Chris Munroe said: "I would like to personally thank Martin and Mark for their tireless and excellent contribution to the club. Two promotions and numerous cup successes in five years is a fabulous testament to them. I wish them all the very best.
“Both can leave with heads held high having done the job they were asked to do.
“The club have taken this tough decision to bring about a change of direction and implement a new structure that will better fit our objectives of continual progression.”
Basford sit ninth in the EVO-STIK League Premier Division and are the league's joint top scorers, though they have the third worst defence in the league.
The club say they will make an announcement shortly on the proposed new structure for the club and an interim managerial appointment, pending a permanent appointment for next season.
They are next in action against Buxton at Greenwich Avenue on Saturday.
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