Pretty much all the analysis says the same: the country is split down the middle, just over 40% want Brexit, come hell or high water while another 40% or so want to remain in the EU, the rest think there are other questions too that merit attention.
Any serious country would decide against a major constitutional change that has the support of just barely half the electorate that bothers to consider the question. Sadly Britain has been a joke for quite a while now.
The only sensible ways out that I see are:
1. Norway+ style Brexit; if Farage et.al. want to leave Single market and Customs union they'll need to campaign for it and win a referendum to leave those - fairly, with no overspending and against a competent campaign calling out their lies.
2. Another referendum, legally binding and with a requirement that losers accept the result and bury the question for at least 20 years.
Neither is likely to happen any time soon, but any other solution will be temporary in nature. Heck, option 1 may not be stable either and I really don't see mr.Democracy-only-works-when-losers-accept-the-result accepting a result he dislikes. He said so before the referendum, but changed the tune since.
There is a nuclear option - No deal Brexit, following the catastrophic crisis for 6-12 months a new deal with EU is signed. It is similar to Norway+, but is more expensive for UK and came at a price of wiping out British manufaturing and services exports. That would be stable, probably, but the price may not be worth paying.
McHrozni