The basic rate of tax could be cut by more than 2p if everybody paid what they owed to the state, Danny Alexander suggested today.
The Treasury Chief Secretary said everyone else had to pick up the tab when the wealthy avoided their obligations.
“We have to make sure that everybody, especially the rich and famous, are paying their fair share of tax,” he told the Sunday Politics programme.
“These sorts of schemes that save wealthy people potentially tens of millions of pounds in tax, they are paid for by everybody else.
“If we could narrow the tax gap in this country by a quarter we could reduce income tax for every basic rate payer by 2p in the pound."
But Simon Walker, Director General of the Institute of Directors said it was necessary to also simplify the tax rules.
"There a more than a thousand specific exemptions tax breaks you can claim...We now have twice as many accountants as we did 15 years ago. We have the highest proportion of accountants in our population in the industrialised world."
Mr Walker called on a straight 35 per cent tax on all income and payments from companies and banks.
Former Prime Minister Tony Blair suggested the public were only willing to tolerate tax avoidance in the good times.
“I think the mood on this has changed,” he said.
“What people maybe would not have cared about a few years back, if you are in a time of austerity people they care about these things.”