The entire question is in the title. Instead of apparating they use the floo network instead. Is floo arrival more impressive than appearing out of thin air? Or maybe that's the point ... it's less frightening?
For the same reason Dumbledore stated here:
“Professor, why couldn’t we just Apparate directly into your old colleague’s house?”
“Because it would be quite as rude as kicking down the front door,” said Dumbledore. “Courtesy dictates that we offer fellow wizards the opportunity of denying us entry.
Of course, the Prime Minister is a Muggle. However, the same courtesy is extended.
It seems like it'd be a massive security flaw if wizards were able to Apparate into the office of the Muggle leader of a nuclear state.
Most likely, the Muggle Prime Minister's office is like Hogwarts, or the Ministry of Magic for that matter: impossible to Apparate into, but accessible using the Ministry-controlled and monitored Floo Network.