Simple: require that beneficial owners (humans) are listed on the title at the Land Registry. These can be private but they must be real. No name, no sale.
I'd favour a more direct approach of simply banning UK nationals from having anything to do with companies in tax havens at all, from Panama to the Isle of Man. No loopholes, no registers to dig through, confiscation if found.
Land reform in Scotland is working on the "beneficial owner" aspect: http://news.scotland.gov.uk/News/Transparency-of-land-owners...
This doesn't force the disclosure of beneficial ownership though. Shares can be held by nominees without that being disclosed on the register. If the shareholder is an offshore company that can also be difficult to trace.
Another fun fact: it's possible to work out the exact most recent valuation of a UK-registered startup by reading its SH01 filing (when it issues new shares). I'm always surprised that the tech press doesn't do this as a matter of course given how excited they get about funding announcements...
Which would make things very awkward, because the United Kingdom is commonly thought of as a tax haven in EU.
(Companies in other EU countries are conducting business in London. Obviously they are doing it for tax avoidance purposes!)
What if I buy a few shares in a publicly traded overseas company, and that company in turn buys a few shares of a company based in a tax haven? Short of making the UK an insular economy, this is not going to happen.
My take would be that the ease of setting up a business in the UK is a great thing for the business people, the general public, and the economy. It is sad that people end up with debts that will never be repaid when a company folds, but without the institution, there would be much lesser chance of a cheap product, gainful employment, or profit in the first place. When a company shields criminal activity, the courts readily bring the people behind it to justice, as the fine article itself mentions. The only going concern seem to be the undertaxation stories repeatedly reported in the press — good rage fodder for the financially illiterate, but they never hold much water under scrutiny.