Taxing global profits
A Kitemark will make precious little difference. This is a problem caused by trying to tax global companies on just their UK operations, and you can't blame them for trying to do whatever is LEGAL to minimize their tax liabilities.
One solution would be to make some big changes to tax law (for example outlawing the unrealistic transfer pricing which is the mechanism used by many of these companies to transfer profits to low tax jurisdictions). I would also stop the use of royalty payments as a mechanism for transferring profits as it so easy for a company to say that it's intellectual property is 'owned' in a tax haven and have bloated royalty payments sent there. These should always be taxed in the country where the revenue is earned. And I'm sure may quite small UK companies do this too, it's not just the big multinational corporations.
But these kind of changes may take years to put into effect, particularly if they require changes to international treaties . A more radical approach would be to offer companies the choice to either pay tax on just their UK business (as now), or to pay tax based on their global profits, taxing a percentage of their global profits in proportion to their UK revenues. Companies could be given an incentive to use this new approach, for example by having differential tax rates (eg 40% using the old approach and 20% using the new approach). This would encourage companies to move quickly across to a 'global' approach to tax while not breaking international treaty obligations as there would still be the option of doing it the 'old' way - at least until the rest of the world could catch up with this new global approach to taxation.
And a company which had no operations outside the UK would be able to submit the exact same accounts as UK-only and as global accounts, so could very easily use the more advantageous global tax rate.