He said: 'I only felt inspired to write it several weeks ago and wondered if my medical colleagues might like to help out by clicking on the link?
'It's a good bit of honest fun! Now will the England results start to improve?'
Dr Whittle is featured on the guitar in the video. He sings alongside Jonny Coulter and The Vale of York Barbershop Club at Tadcaster Social Club, North Yorkshire.
It was filmed two days before England drew 1-1 with the US.