How could anyone besides them prove effectiveness or ineffectiveness of this campaign? I don't think it's possible. At the very least, the side they supported won (Brexit) and they should not be trusted.
Leave.UK was accused of violating electoral law. I believe the Electoral Commission has now dropped its investigation.
Incidentally, to break UK law, you usually have to perform the violating act in the UK (we have a few laws that involve extraterritoriality, but they are far and few).
Faceache barely does anything in the UK. They apparently make no money here; they don't sell stuff (not even advertising - that would be the Republic of Ireland). CA collected data on US citizens; that's legal here (and would have been of very little interest to Brexit campaigners). As far as I know, nothing CA did violated UK or EU law.
You say "the side they supported won (Brexit)". Do you mean that Faceache supported Brexit? I don't think they had a dog in the race at all. Or do you mean CA? It's been argued that CA took money to provide services to Leave.UK, but that's not the same as saying they supported Brexit.
Trying to "swing elections" is legal in the UK. In fact it is encouraged; people who successfully swing elections often get appointed to important positions such as Prime Minister. It's completely legal to hire polling companies to help you better understand the voters. It's completely legal to hire advertising companies to promote the electoral outcome you want promoted.
Now you are speaking of trust; of course, I trust neither CA (now defunct) nor Faceache. But Faceache did not drag my country into wars in Iraq, Libya and Syria. Faceache did not have that much power. The UK joined those wars largely because of diplomatic pressure from the USA - a much more powerful entity than this rather tedious online advertising company.
From what I have read, and despite their bragging, CA wasn't even helpful to the Leave.UK campaign. Their data wasn't relevant, and anyway Leave.UK didn't have the organisational capacity to make use of whatever data they could offer.
https://www.theguardian.com/politics/2018/may/11/leaveeu-fin...
You are correct that they haven't (been charged with having) broken electoral law in the UK, but they have broken data protection laws in relation to the information which was then used by Cambridge Analytica:
https://www.theguardian.com/technology/2018/jul/11/facebook-...
Whether that information was then used by Cambridge Analytica as part of a Brexit campaign is open to more questions.
Facebook is an echo chamber. People don’t go there to be informed; they go there to validate their already held beliefs. Given the large ideological chasm between the two candidates in the 2016 election, it defies logic that even a single voter was swayed or chose not to vote at all based on ads they saw on Facebook.
https://www.washingtonexaminer.com/weekly-standard/the-elect...
Of course it's impossible to say whether Trump would have won even if he hadn't spent any money on Facebook ads, but we're talking about a campaign that spent hundreds of millions of dollars in total. If this amount of money doesn't include enough to influence 78k people to go out and vote for a specific candidate, then we might as well give up on the very concept of advertising.
[1] https://www.washingtonpost.com/news/monkey-cage/wp/2018/03/2...