For all physical products sold the UK, the taxman gets 20% of the price as VAT. That's more than your 10%, so done.
Also, for all companies employing people in the UK, the company pays the taxman money for payroll taxes (employer's NIC, "employees" NIC, income tax) for all their UK employees.
The concern here is taxes on _profits_, and multinational companies can change where their profits happen to benefit from lower taxes. If Apple employees in California design a new iPhone, it's built in China, imported via a port in Holland, it uses online services from servers in Ireland, it's marketed by a marketing team in France, and it's sold by a sales team in Germany to a shop in the UK that in turn sells the phone to a customer in the UK, all the above funded by stocks and bonds issued in the USA, then where should the profit be recognized? Do you allocate some of the profit to each of those countries? Heck, how do you even figure out the profit - e.g. how much of the design & marketing cost gets figured against each sale, etc. The answer at the moment is that lawyers and lobbyists and politicians get involved, and the corporation can fudge things however it wants.
In my opinion, corporation tax should be abolished, you can just set VAT and payroll taxes to fair tax rates and be done with it, and everyone pays the same percent of turnover. That's not possible to fudge.