According to *The Concise [New Patridge Dictionary ][1] of Slang and Unconventional English* the humorous expression dates back to 1985: 

> - **more tea, vicar?** used humourously to acknowledge a fart or a belch, UK 1985.

(probably from a sitcom popular at that time)


  [1]: https://books.google.it/books?id=h0mcBQAAQBAJ&pg=PA527&lpg=PA527&dq=more%20tea%20vicar?%20%20first%20usage&source=bl&ots=_JtRS1oR0e&sig=-VTKFmA1CrRH48gnKYzXRdYvWr8&hl=it&sa=X&ei=UCctVdWbKsGcPPuogOAB&ved=0CGgQ6AEwCQ#v=onepage&q=more%20tea%20vicar%3F%20%20first%20usage&f=false