The pair, who once worked at City under Andy Leader, have turned Alresford from Wessex League also-rans into one of the top clubs in the league.
Alresford’s 3-0 win at Whitchurch earlier today put them five points clear at the top of the Premier Division, though Sholing have four games in hand.
Winchester were searching for a new manager after Neil Hards recently informed the club that he was stepping down at the end of the season for personal reasons.
Alresford tonight released a statement from chairman Trevor Ingram and secretary Keith Curtis.
It said: “Two weeks ago the Chairman of Alresford Town, Trevor Ingram, was informed by Tim Cole that he intended retiring at the end of this season due to family pressures.
“In light of this information, the Chairman asked co-manager Danny Robinson what his intentions were for next season and he indicated that he felt he wanted to try management at a higher level and needed a new challenge – possible clubs were Thatcham and Wantage, both of which would be closer to home.
“The Committee, therefore, began discussions about finding a suitable replacement but did not inform the players as they did not want the disruption to affect their performances with important games to play.
“Last Saturday (April 12) the Chairman received a text from David Malone of Winchester City informing him that he was intending to contact Danny and Tim about the impending vacancy at Winchester City.
“Tim Cole rang the Chairman within days and informed him that they both intended to take up the role at Winchester City.
“The Chairman requested that this information be kept from the players until the completion of our fixtures, which they agreed to do.
“However, following the completion of the Aldershot Senior Cup Semi Final three days later, on Thursday April 17 they informed the players of their intention to leave and where they were going to, directly contravening the request made by the Chairman.
“In light of this the Chairman and Secretary of Alresford Town FC had a meeting with the players following the completion of their victory over AFC Portchester on Saturday.
“They explained the above sequence of events and that the search for suitable replacement(s) was underway.
“As far as Alresford Town FC was concerned, the club would do everything possible to keep the team together.
“The club would understand if some players wished to play at a higher level, but felt that it was important to try and keep the majority of the squad together if possible as their achievements over the last two seasons have been tremendous.
“Their record is an indication of what can be achieved without any form of playing budget.
“They were also told that the club would not seek to play at Step 4 as we did not think it is a viable option in view of the costs that are incurred.
“We did not want to follow the likes of Sholing or Thatcham.
“The search for candidates for the vacancy will now be stepped up and we are hopeful of making an announcement in the very near future.”
Robinson and Cole last season led Alresford to a trophy treble of Hampshire Senior Cup, Wessex League Cup and North Hampshire Senior Cup.
They have already retained the North Hampshire Cup this term and are through to the final of the Wessex League Cup.
As well as also being top of the Wessex League, they are also through to the final of the Aldershot Senior Cup.