The Doctor getting a 20th Century musical act to perform in another century is nothing new.
In a Seventh Doctor novel called "Happy Endings", his 25th Century companion, Professor Bernice Summerfield (she's an archaeologist too!) meets a guy in the year 2010 and decides to get married.
She has often told the Doctor that she loves everything 20th Century, especially the music, and that the Isley Brothers are her favourite musical act. The Doctor takes the Tardis back to 1966 to a London hotel the Isley Brothers are staying in, and persuades them to perform at Bernice's wedding.
He takes them forward in time to 2010 and plays them a copy of their recording of "Summer Breeze", which they are not familiar with as they will not record until the seventies, so he asks them to learn it and perform it at the wedding, which they do.