Sure, let me try to give you some context.
The mainstream political parties in the UK since the 70s were pro-EU, though with some muttering at the fringes. Among the general public there was a bit more ambivalence. Anti-EU sentiment was generally written off as racist, stupid etc etc and this wasn't necessarily wrong because the loudest voices were parties like the BNP - basically 'out' fascists.
This changed with the accession of central and eastern european countries to the EU. <ost western EU countries imposed a two year stop on free movement but then Tony Blair wanted to "rub their noses in diversity" (referring to the sceptics) and opened the doors to the UK on day 1. Immigrant populations became much more visible very quickly and as a result so did anti-EU parties like UKIP. When a woman asked the next PM, Gordon Brown, something about migration, he was caught on a microphone he thought was deactivated saying something about "that bigoted woman" and the flames were fanned ...
2010s - the UK has a coalition and to curry favour with the eurosceptic side of the electorate the conservative prime minister, David Cameron, goes into the 2014 election promising a referendum. He's still sure it's a fringe issue and once people have had their say on the matter UKIP, (who are starting to eat 'his' vote share on the right, will be neutralised and we can all stop talking about it. This had worked for him twice - in coalition he was forced to run one on changing FPTP to AVC voting and through a campaign that I think was run on disinformation he managed to head off any further discussion on democratic reform. He also granted the Scottish government's wish to hold an independence referendum and then successfully campaigned for a "remain" vote there. He was on a roll.
So he calls the EU membership referendum.
The terms are set - a simple in/out question. It was legislated as a guiding referendum rather than a binding one. The difference is that the act of parliament introducing the referendum on AVC already contained legislation that would have been triggered the next day to change the voting system if it had passed. Power was actually delegated from Parliament to the people in that case. In contrast the EU referendum and the Scottish Independence referendum were more like national opinion polls - they didn't establish anything in law beyond the result itself.
So when the official Leave (https://en.wikipedia.org/wiki/Vote_Leave) and Remain (https://en.wikipedia.org/wiki/Britain_Stronger_in_Europe) campaign groups were established, that was their sole mandate - get information out there about your position, get people voting. They weren't the only campaign groups, but they were the official ones.
The PM and his whole cabinet are pro-business, fairly socially progressive conservatives. Definitely pro-EU. As are the main figures in the Labour party (mostly). So the establishment all rally behind the remain campaign. It is assumed that there will be an easy, comfortable win for remaining even among hardcore leave supporters. Despite the referendum being advisory/guiding, David Cameron says that a vote to leave will be acted on immediately with no plan or preparation to try and scare people into voting remain. When opinion polls start to look a little bit dodgy, the chancellor threatens the country with a punishment budget including big tax hikes if leave wins. The spectre of uncertainty is raised repeatedly but in the end that gives ammunition to the 'leave' side who call it out as "Project Fear", a term the pro-independence scots had coined to describe the 'remain' campaign in their referendum.
> Maybe having an abort clause instead of jump off the cliff if the bridge isn't built yet.
> Maybe the referendum should have required the government to build the plan which would be decided on later.
So thats the thing - the law that created the referendum didn't include any requirement or any plan to do anything whatever the result. The way the whole shebang was run, nobody had the power or the mandate to make a plan because the referendum was advisory and was really only meant to be for show. The real plan was that on the 24th of June 2016 David Cameron could address the nation and say "See, we told you, the British people have spoken, shut up about the EU, let's get on with our lives".
But when you as Prime Minister call a referendum and promise (or threaten) that the result will be carried out post-haste, even when you have quite deliberately not set out a course of action or legislated for it, and you lose ... you've backed yourself into a political corner and you basically have to do it.
Which is why he resigned the next day.
And that's why there followed years of parliamentary arguments, court cases and in-fighting about what the hell to do next. You can't just throw that sort of thing aside. If over half of the people who voted, voted to leave, it's probably electoral suicide to ignore it and you're paving the way for UKIP to rise. You can't ask for a do-over, because there's a perceived history of the EU getting people to re-vote on important issues (Ireland, Denmark IIRC(?), to do with referenda rejecting the new EU constitution/Treaty of Lisbon) and the 'leave' side would have had a field day portraying the whole edifice as profoundly anti-democratic. But the majority of the people who are tasked with coming up with a plan don't want to do it. Eventually the government collapses, but the conservatives are re-elected on a promise to "get brexit done", which brings Boris Johnson to power and gives further political mandate to leaving. Through a variety of political manoeuvres, some questionably legal, a plan is finally approved and put into action four years later.
Sorry for the wall of text :)
Anyway, all of that is to say that while Brexit may well be the greatest act of political self-harm the UK has carried out in a good long while, that's why I feel the specific criticism that "You voted for something when there wasn't even a plan you dumb shits!" isn't really fair. There was never going to be a plan, and if they didn't vote for it there was probably never going to be another chance.
tl;dr - there wasn't a plan because the people with the power to make one didn't want one.