The first referendum was not valid as Vote Leave campaigned illegally.
The Vote Leave campaign was proven to have lied extensively about the benefits of Brexit. But beyond that, it actually broke election laws in its spending. It deliberately did not disclose the full extent of its campaign spending and after a full investigation, the Electoral Commission found it had exceeded spending limits.
The Vote Leave campaign employed a litany of underhand campaigning tricks to get voters to back Brexit. Not only was there the high-profile claim that once Britain left the EU it would have an additional £350 million per week to spend on the NHS, but it also gave hundreds of thousands of pounds to a firm linked to Cambridge Analytica.   Following a comprehensive investigation, Britain’s electoral watchdog, the Electoral Commission, fined Vote Leave £61,000 for exceeding the spending limit of £7 million by some £500,000. It still remains to be seen in what other ways Vote Leave campaigned in breach of British law. An inquiry is still being carried out by the Information Commissioner’s Office investigating Vote Leave’s use of voter’s personal data. It may yet find that Vote Leave breached more campaign laws. Given the findings, it is clear that the Vote Leave campaign behaved illegally. Therefore, the first referendum cannot be considered fair or legitimate. The only logical move would be to have another referendum in which both sides campaign within the Electoral Commission’s legal guidelines.
The Electoral Commission is not exactly an impartial institution in this case. Arron Banks, Vote Leave’s founder, called the commission’s decision to fine Vote Leave, “a politically motivated attack on Brexit”. He also suggested that the commission was comprised almost entirely of remainers, rendering the institution entirely unfit to investigate Vote Leave and oversee the Brexit referendum.
Vote Leave broke UK laws regarding campaign financing. Therefore, its referendum victory is not legitimate. Therefore, there should be another legitimate referendum.
Vote Leave did not break the law. The body that suggested it did was not impartial.