The decision by Starbucks to voluntarily pay £10m in taxes in each of the next two years has come under fire from critics who say the move makes a mockery of the tax system, while the tax authorities reaffirmed that corporation tax was not voluntary.

Prem Sikka, professor of accountancy at Essex University, criticised "private sweetheart deals" with HMRC, saying this would send a bad signal to other businesses.

On Starbucks, he said it was important to know to which part of the past years the £10m figure relates. He told the BBC Radio 4 Today programme on Friday: "The last four years they declared a loss of about £145m, so are they saying this £10m relates to the past four years?

"It is a practice of HRMC also to charge interest and penalties for late payments. How exactly is this £10m arrived at? We have absolutely no idea and really Starbucks should publish all its tax correspondence and the tax computation so we can all see."

Sikka said it should be a standard requirement for all multinationals to allow the public to see their contributions to the public purse.

"We should really get them to publish a table which shows the jurisdictions they are operating from. What their sales are, the costs are, their employees are, and the taxes they are paying in each country. So if we find a company that is booking about $16bn of tax revenue in Ireland with only 80 staff, we should be highly suspicious. We haven't really reformed anything about corporate accountability."

Tory MP John Redwood said the best way of getting more revenue was by cutting taxes, as well as pursuing "very strongly" those who break the law.

He told Today: "The higher the tax rate a country seeks to impose, the more tax avoidance there will be, and the lower the rates – which is the way the coalition government is going – the more income I think will be put into our country as a result.

"There is a competition between the main jurisdictions of the world to be able to tax profits and obviously the countries with the lower rates tend to win, because there is quite a lot of scope to switch income around for legal purposes."

He added: "The transfer pricing – where you buy things and how much royalty you pay within the business – is always a difficult set of questions. They don't avoid profit tax overall because the profit comes out somewhere. They are discussing where they should put the profit. They would obviously rather do that in a lower tax jurisdiction if that fits the facts sufficiently to satisfy the tax authorities."

Redwood said Starbucks also had to satisfy its customers and the wider community to maintain its business and "that's why they made the decision they made".

Sikka said corporation tax in the UK had fallen over the years from 52% and is heading to 21%: "So this idea that lower corporation tax rates somehow makes us more attractive doesn't hold water."

Corporation tax is levied on profits but Starbucks has avoided paying the tax for three years in the UK through complex international payments within the company known as transfer pricing.

Starbucks currently makes a loss due to a 4.7% premium paid to the Netherlands division – where its coffee beans are roasted – and another 20% premium to Switzerland to buy the coffee beans. The company said it would not claim deductions on these payments, or against intercompany loans.

The unprecedented announcement by Starbucks was made at the London Chamber of Commerce, where Kris Engskov, the managing director of Starbucks UK, said: "I am announcing changes which will result in Starbucks paying higher corporation tax in the UK – above what is currently required by law.

"Specifically, in 2013 and 2014 Starbucks will not claim tax deductions for royalties or payments related to our intercompany charges.

"In addition, we are making a commitment that we will propose to pay a significant amount of corporation tax during 2013 and 2014 regardless of whether our company is profitable during these years.

"These decisions are the right things for us to do. We've heard that loud and clear from our customers."

Although he said the tax authorities were unaware of the company's plans, he added they had been in general talks.