I'm pro-European, but I would argue that pulling out of Europe to force accounting for UK sales to occur in the UK legal domain might be a very good start.
At least this way each country would be incentivised to enforce tax locally in a controllable and predictable way. And I'm sure that whilst some companies might wish to pull out, most would stay.
a profit is a profit, it may be less than before but if you're still creating profit you wouldn't give it up.
That would actually have the opposite effect: corporations would simply "optimize" even more around the UK system, and it'd be easier for them to push money even further away from the reach of UK authorities.
What is needed is a strong European effort to align taxation, which would remove any benefit from schemes like the Double-Dutch and Double-Irish, and then levy heavy taxes on capital flight outside European borders. This, of course, if our elites actually cared about tax evasion, which they really don't -- can't risk to find those revolving doors shut when it's your turn to bow out.
Nothing about it is grey hat. The techniques for a global business to shift taxes into a low tax country is well known in an global tax planning group.
Accounting like this is very much like (grey-hat?) hacking; you have a very large and complicated system and you simply need to find the weakest spot.
Defending against that can't really be done when you only have control over a single component of that system.