Unconstitutional: The United Kingdom is comprised of four countries - England, Northern Ireland, Scotland and Wales. Constitutional-level alterations to the UK require unanimous approval from all four countries, but, in the 2016 referendum of membership of the EU, Northern Ireland voted Remain by 56% and Scotland by 62%. Brexit only had a mandate in England and Wales.
Undemocratic: Because of population differences, even if every one of the 10.2 million people in Wales, Scotland and NI voted against a piece of pro-English legislation, only 10% of England would have to vote for it in order to force it on the other three, because England's population 55.3 million. 87.2% of all Brexit voters were in England. A referendum is always "the will of England" rather than "the will of the UK".
The UK signed the Venice Commission's 2006 document on how to run a referendum along democratic lines. Section 2.3 clearly states that a referendum is only democratic if minority countries (NI and Scotland) are not forced into decisions by a majority nation (England).
No consensus, no 'will of the people': 37% voted leave, 35% voted remain and 28% remained. The victory margin is not enough to force through changes of this magnitude. Before the referendum, Leave campaigners created a petition arguing that if the majority was less than 60%, then, the referendum was not a valid indicator of the will of the people. The result was below this threshold.
Misinformation: There was no informed vote: The UK's citizens are the least knowledgeable about the EU and have suffered from many high-profile long-term campaigns ran by sensationalist newspapers with anti-EU agendas. The Leave Campaign Director Dominic Cummings admitted in 2017 that the Leave campaign relied on lies and misinformation.
The Leave Campaign Was Illegal: The UK</a>'s House of Commons has found that the Vote Leave campaign committed "serious breaches" of campaign law, with millions poured in by anti-EU foreign government and anti-democratic institutions in Russia. Cambridge Analytica illegally influenced an uncountable number of people with targeted misinformation based on data obtained from a Facebook data breach. Vote Leave intentionally broke electoral law by donating hundreds of thousands of pounds to avoid spending limits and Leave.EU has also been found guilty in court of committing four electoral offences during their own campaign. Illegal overspending influenced "tens of millions" of people, and statistics show that it directly led to over 800,000 people changing their minds, changing the result of the referendum.