Mike Down, of accountancy firm Baker Tilly, said the HM Revenue & Customs (HMRC) should be checking tax returns to see whether individuals had already explained their circumstances.
He told the Daily Telegraph that The Revenue is "adopting a computer says yes approach, rather than simply checking the tax returns".
One case involved an elderly widow whose effective tax rate was low because she was giving more than half her income to charity.
More top news
Sir Bruce Forsyth, Sir Cliff Richard and the Prime Minister have been among those paying tribute to Cilla Black following news of her death.
TV favourite Cilla Black, who has died aged 72, gave viewers a "lorra, lorra laughs" during her long career.
Some rain in the north. Very warm sunshine in the south