The chief of the taxpayer-owned Royal Bank of Scotland will receive a bonus worth almost £1m, despite a cap imposed by the bank's board.

RBS chief executive Stephen Hester is in line for around three million shares, about half his entitlement, which equates to between £800,000 and £950,000 at yesterday's closing share price, Sky News said. Hester, who is on a salary of £1.2 million, last year received an all-shares bonus worth £2 million.

The board of RBS, which is 83% state-owned, is understood to have agreed the payout, which will be paid entirely in RBS stock and deferred for three years, at a meeting yesterday.

PM David Cameron has made it clear that he would regard a bonus of more than £1 million for Hester as unacceptable.

RBS declined to comment on the report.

The decision, which could be confirmed as early as tomorrow, comes after Business Secretary Vince Cable unveiled proposals to crack down on hefty salaries and bonuses, including binding votes for shareholders and improved transparency.

However, RBS's concession on Hester's bonus will not defuse the row over directors' pay completely, as John Hourican, head of RBS's investment arm, who will oversee a restructuring that will include around 3,500 job losses, picks up £4 million in long-term incentive shares that he was awarded in 2009.

RBS is believed to be holding discussions with UK Financial Investments (UKFI), the body which manages the taxpayer's stakes in Britain's bailed-out banks, about its plans.

Last week, RBS and Cameron denied a newspaper report that the bank's board was proposing to award Hester a bonus of up to £1.6 million.

The payment protection insurance (PPI) mis-selling scandal, for which RBS set aside compensation of nearly £1 billion, is understood to be among the factors taken into account by RBS's remuneration committee when deciding his bonus.

Britain's biggest banks are expected to unveil their bonus plans next month when they publish their annual results.

Antonio Horta-Osorio, chief executive of part-nationalised Lloyds Banking Group, announced he would forgo his annual bonus of up to £2.4 million following his two-month leave of absence and a rocky period for the banking giant.

Elsewhere, reports have suggested Barclays boss Bob Diamond could receive a £10 million payout in the forthcoming bonus season.

The Barclays chief executive - who was once dubbed the unacceptable face of banking by former business secretary Lord Mandelson - could receive a share award worth as much as seven-and-a-half times his £1.3 million salary.