I can't say if the latest regulations have really made an impact. They have surely made banking in EU a lot more bureaucratic and a lot more expensive for a small business.
The last Commission President was literally the ringleader for tax theft: he was FM/PM of Luxembourg, and actively lobbied companies to domicile there, funnel revenue through Luxembourg (i.e. structuring for tax avoidance alone), and personally negotiated the 1% corporation tax deals.
...it always amazes me how little people actually understand about the EU.
Btw, the main issue for the Conservatives has been their inability to force the overseas territories to do things (what they actually think about tax havens is irrelevant now, events have moved on).
This has changed though, as certain European parties' voters have become irate about international tax evasion. For center-left PMs, stomping down on countries like Cyprus isn't going to lose them any votes and increasingly looks like a political win.
For Britain, the conundrum is that there's so much British money in the "nearshore" tax havens of Channel Islands and the Isle of Man. Whereas Luxembourg mostly cut sweetheart deals for corporations and Cyprus mostly dealt with non-EU foreigners who don't get to vote anyway, cleaning up the British tax havens would threaten the hidden wealth of Conservative voters directly.
The only way to avoid tax is to permanently move there. And, if you are familiar with either of those locations, you should know that the punishment fits the crime.
Also: it is far bigger than Luxembourg and Cyprus. Malta is basically a haven for financial fraud. Ireland is basically a tax haven now. And basically all of the East European nations are targets given the weak controls of their financial institutions (and Denmark as it turned out).
Having lived in the UK, I'm convinced that the real reason for Brexit is to preserve these offshore tax havens from any meddling by EU regulations.
It's not an accident that Brexit suddenly became crucially important to the Conservative Party only when the EU developed a new interest in unified financial regulations after all the turmoil of 2008-2011.