No it's not, it's up to the government. What people keep forgetting is that a referendum isn't voting a group of people in power. The reasons why people vote one way or another might be completely different from the ones argued by the (main) campaigners on that side.
The government has asked the people a question on how to deal with that matter, and they've gotten an answer. When you ask somebody if he wants some tea, you have to get that tea yourself when he says 'yes please'. Not say 'Fuck that, tea is bad for you, I'm leaving, I'm sure my replacement will get you your damn tea'.