Why didn't the British government have a plan for brexit. Are they a bunch of amateur hacks?

For the past 30 years, successive British Governments have had no plans for what to do as part of Europe. We could have helped make it work, but instead we stood in the doorway shouting that if we didn't get our way, we'd take our toys away. It's hardly surprising that there were no plans for what to do if the nation (or half of it at least) decided to call Cameron's bluff.

OK We have a wrecked economy, a government only a third of the electorate voted for (far fewer than voted Remain), a poisoned relationship with our main trading partners, racists attacking anyone they don't like and a non-functioning opposition. Very shortly we're going to get a prime minister we don't want imposed on us. Is this getting our sovereignty back? It's time we chucked the whole bloody useless lot of them into landfill and started from scratch.

Simple, They thought that the remain side was going to win. David Cameron only decided to do a referendum to prove everyone wanted to stay in the EU after a petition was made on the government website a few years ago. They never expected it to backfire (weren't they wrong). That's why there was no planning. They thought the leave side had no chance

Because when David Cameron said he'd hold a referendum, the papers were saying he had no chance of winning the election when lo and behold he did, the press wouldn't let him get away with doing a U Turn on something as big as a EU Referendum so he had to hold one and the rest is history.

They didn't seriously think anyone would be dumb enough to vote for it.

There was a vocal faction within the conservatives calling for Brexit- in the end Cameron decided to hold a referendum basically to shut them up and having things go back to normal, not realising millions of people would actually vote to leave.