Starbucks is voluntarily paying more taxes than they should in the UK because of political pressure. Political pressure companies can usually handle, except if it leads to loss in revenue. In the case of Starbucks it was obvious; UK customers avoided the US coffee shops and started to drink their coffee in English coffee shops. That hurts. The Politicians were double successful in attacking Starbucks; they received additional tax revenues and excercised protectionisme without anyone objecting. Except for Starbucks obviously.
What did Starbucks do? They established a Dutch company that owned the Starbucks trademark probably for all non-US coffee shops. This can be achieved multiple ways, because the trademark is a US trademark. Either the Dutch company paid for the use of the trademark by means of a one time payment, or they have to pay an annaul license fee to the US owner of Starbucks. The IRS likely attacked this structure and demanded either a higher payment from the Dutch company (leading to US taxation ) or a higher lincense percentage or annual payment to the US Starbucks trademark owner. In both scenarios the IRS would benefit.
The result of this set-up is that the UK Starbucks coffee shops need to pay the Dutch company for the use of the Starbucks trademark in the UK. That HRMC feels that Starbucks is not paying enough UK corporate income tax is cynical, because the UK concluded many tax treaties including a treaty with The Netherlands. Starbucks applied the tax treaty and if the UK do not agree with the consequences of the application of this treaty they should renegotiate the treaty. What they did now is bypassing treaty law and abusing internationally agreed tax principles.
