"A Bridge Over You is a rework of Fix You by Coldplay and Bridge Over Troubled Water by Simon and Garfunkel.
Proceeds from sales will go to health charities including Carers UK and Mind.
The song is available now but the NHS choir that recorded it is asking people to wait download it until December 19 so that it counts towards the Christmas chart.
The Lewisham and Greenwich NHS Choir - made up of staff from across the NHS workforce, including doctors, nurses, physiotherapists, porters and administrators - recorded their tune after becoming the runners-up in Gareth Malone's BBC2 TV series Sing While You Work.
They want to raise awareness and celebrate the good work of the NHS.
Choir member Caroline Smith, a children's community physiotherapist, said: "The NHS is not perfect but it's an amazing service. We are very lucky that we have it.
"Everybody uses it and doctors and nurses will be working on Christmas Day. The song is really special and reflects the jobs NHS staff do. If people buy the single it would be an amazing thank you to know that people appreciate the NHS."
NHS staff have released a charity single that they hope will be this year's Christmas Number 1.