Wilkinson went on to say: "I would like to thank Ian, the Board, the staff, the players and all the supporters who have been with me for an amazing seven years. It's been an unbelievable seven years here, but I have been thinking that my time was up a couple of weeks ago. Today I have made the decision to take a break and stand down and see what happens next.
"I want to make it clear, that this isn't a decision I have taken lightly, I have never quit before."
Assistant-manager Jamie Leacock and coach Mike Percival have also left the club.
Chairman Ian Passey said: "It's a bit of a bombshell to be honest and now we need to move fast in time for our next game on Saturday against Gloucester City, I need to speak to the board and we will release something as soon as possible."
Club captain Matt Day said: "We are gutted, but we will stay together as a team".