I'd say that it's a complex process which is going to take a lot of time and money to sort out. That said, because it's the "will of the people", I'd set up a very high-profile department to look into it and give regular, non-soundbite reports. Meanwhile, I'd begin to address immigration (anything would do as long as it got some kind of result). Over time, the money it would cost us to exit and the potential economic impact would get big headlines. I'd also talk to the EU to have a go at reforms and talk up any that were achieved. In about 10 years, assuming I'm still in power, public opinion would have changed.
In short, look as through I'm doing everything possible to achieve an exit and mount an honest, fact-checked comms campaign which tells the truth about what it's actually going to mean for the country. Continue until the country understands that. There would be no buses involved.