The Railwaymen confirmed the departure of Carnell, pictured, for the Puritans on Monday night in a statement on the EVO-STIK League Southern South & West club's website wishing him well and hailing him as a "consummate professional".
A club said: "The club can tonight confirm the departure of Club Captain Luke Carnell to Banbury United. Didcot Town would like to wish Luke Carnell all the best as he makes the step up to the Evo-Stik League Southern Premier League club. Luke is the consummate professional in all of his dealings with DTFC and we will be sad to see him leave the club.
"However, the club would never step in anyone's way to progress to a higher level of football. Luke is certainly more than capable of acquitting himself higher up the pyramid and we wish him all the best in his next chapter in football and beyond."
Officials at the Draycott Engineering Loop Meadow Stadium also asked fans to back manager Andy Ballard ahead of their trip to league leaders Hereford on Saturday after the latest blow to his injury-hit fifth from bottom squad.
The club added: "Unfortunately, the departure of Luke leaves us with a significant headache as Luke's boots will be very difficult to fill. Manager Andy Ballard is actively pursuing all avenues to improve on the squad we have, which in recent weeks has been hit severely in by absences, injuries and player departures.
"The club will continue to support Andy, Ian Lovegrove and his management team to restructure and improve on his squad through this spell as he looks to turn around results. Whilst we can understand supporter frustration over recent results and our current league position, we would like to request patience during this period of transition and hope our loyal supporters get behind the team to help us get back on track and climbing the league table."
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