He added the force was working with national and international agencies to find Tshuma.
“We are urgently working to find and apprehend him, and would appeal to him directly to hand himself in.”
He appealed directly to the suspect, saying: “Mark, unthinkable harm has been caused to those around you and this has left your relatives and friends utterly devastated. Criminal investigation knows no borders.
“Please do the right thing, come forward and hand yourself in to local authorities.”
The house in Carnoustie Drive, Great Denham, has been cordoned off and bunches of flowers have been placed on a hedge outside.
A woman who was among the people who laid flowers tearfully said: “We’re really sorry to lose her.
“She was such a gracious mother.”
Other neighbours who spoke to the BBC said they were shocked the incident took place in “such a nice and safe area”.