Britain is characterised by both a pragmatic able sensibleness, and inward-looking narcissistic post-imperial nostalgia. The latter finds the EU a symbolic humiliation, the former gets on with engaging with its benefits and influencing its development. However, because of the inward-looking nature of British/English exceptionalism, visibility of the advantages of the EU, and an understanding of it and its operations, are distinctly attenuated. Reap the benefit of the single market, but still think Johnny Foreigner is somehow less than the world-straddling Empire Brit.
This means there has long been a persistent pool of resentment about the EU, and a lack of understanding of its benefits.
Calamity strikes when idiot Cameron attempts to placate the monster with a referendum. Not only does the government get a well-deserved kicking for unrelated reasons, but the Remain camp is utterly unable (unwilling?) to communicate the real and symbolic advantages of the EU.
But to win, the campaign has to propose an alternative that is better than EU membership. Consider it as on two dimensions, advantages of membership (mainly but not just economic) versus the glory of buccaneering independence: trade off damage of leaving with the advantages of freedom. People will weigh the dimensions differently, but a best-of-both-worlds was inevitably sold (stay in the single market, exact same benefits, keep out immigrants, free-trade deals with god knows who). The reality is different: first, the EU negotiates effectively, so you’re only going to get advantages at the cost of suffering, or avoid suffering by making major concessions; secondly for many people the advantages of membership were not properly accounted for. In other words, the spectrum of available deals is much less attractive than campaigners promised: from worthwhile independence coupled with crippling damage, to minimal damage with trivial levels of no-influence-rule-taking independence that act as a permanent reminder that Brexit was an idiot’s project.
From a certain point of view, the only people for whom there is a good Brexit are (i) those whose desire for gutting human, worker, and consumer rights, or (ii) those whose empire-nostalgic xenophobia, is sufficient to make the economic damage worthwhile. Thus the range of available Brexits only includes benefical outcomes for people with extreme values. A large part of the spectrum consists of outcomes that are worse than membership for a large part of the polity. The only thing that makes the politicians continue is the weight given to respecting the democratic mandate (which, while not inviolate, is a considerable issue).
But this yields the action problem: (for most people) there is no good Brexit, so it becomes very difficult to operate. There is no point in negotiating properly because the best you can do is worse than remaining. For some, of course, negotiation will only prevent the only Brexit with a political premium, i.e., car-crash No Deal, so undermining negotiations is in their interest. For the rest, it is hard to muster the political will to make a serious attempt to achieve a viable Brexit.
This I think explains why the negotiations have gone nowhere, and why the British establishment is completely rudderless and at war with itself, going around in circles looking like utter spoofers. There is no good outcome available: exits via car-crash no-deal or Brexit in Name Only, or revoke. And revoke isn’t viable because of the real weight of the respect for the democratic mandate.
That’s why they’re burning the extension doing stupid stuff like a leadership election, and choosing Boris Johnson.
tl;dr: Stupidity got them into a situation where there is no good exit, and a combination of stupidity, pride and greed is making sure they stay there.