Barclays said a third-quarter haul of £1.5 billion helped profits more than double in the first nine months on an adjusted basis, while HSBC reported results “significantly ahead” in the quarter to September 30.

The pair, which have avoided turning to the Government for state aid, gave hope that bad debts among recession-hit borrowers were starting to level off as they reported sharp quarter-on-quarter falls in impairment charges.

Barclays reported £4.54 billion in profits for the first nine months of the year - down by nearly a fifth against a year earlier.

But the group said the result more than doubled on an underlying basis as it had enjoyed “consistent profitability” so far in 2009.

HSBC added that, on a reported basis, its third-quarter figures were lower than a year earlier, with both banks being impacted by tightening in credit market spreads.

However, it too posted improving underlying figures as the two banking heavyweights began to put the troubles of last year’s financial crisis behind them.

Concerns are mounting that the better results will see the return of excessive bank bonuses.

But Barclays and HSBC sought to assure that decisions have yet to be made on full-year payouts and will take current fears into account.

Barclays said bonuses were accruing at a “broadly consistent” rate to prior years, although it claimed this did not mean it was reverting to former bonus policies.

It has already signed up to international G20 rules on pay reforms which recommend clawback clauses and deferral over a number of years.

The bank is also talking to major investors over bonus pool levels ahead of its year-end decision.

“We will be fully compliant with the G20 rules in considering bonus amounts and we will be thinking of all our stakeholders - employees, shareholders and the broader community - and we will be taking into account all of their views,” said the bank.

HSBC, which has also agreed to the G20 recommendations, said it would pay “appropriate” levels, “at the same time being conscious of the environment in which we are operating”.

Bad debt levels are showing encouraging signs, according to both HSBC and Barclays.

HSBC has been hit hard by the so-called impairment charges and was the first of the banks to flag up the start of the credit crunch, given its huge exposure to sub-prime mortgage borrowers in the US.

The group posted bad debt charges soaring by 39% to 13.9 billion US dollars (£8.4 billion) in the first half and it has been slashing costs to counter market pressures - only last week announcing another 1,700 job cuts in the UK.

But it said that its bad loans fell to the lowest quarterly level since the second quarter of 2008.

Barclays said it believes impairments will now peak sooner than first thought, at the end of 2009 or first quarter in 2010 as the global economy begins to recover.

While it is still seeing the impact of bad debts and credit market writedowns, with impairments totalling £6.2 billion in the first nine months, quarterly figures show a marked improvement on the beginning of the year.

The banks are likewise benefiting from bumper results in investment banking as they take advantage of currency movements, interest rates and credit spreads.

HSBC said its global banking and markets arm was enjoying a record year.

Barclays said its Barclays Capital operation, which is led by president Bob Diamond, helped drive a 26% leap in income to £23.8 billion in the first nine months of 2009 - more than for the whole of 2008.

The bank is benefiting from a beefed-up BarCap in the wake of its takeover of parts of bankrupt US rival Lehman Brothers.

However, shares in the two banks saw mixed fortunes on the FTSE 100 Index as investors registered disappointment that BarCap’s results were slightly weaker than hoped.

Barclays stock fell 2%, while HSBC rose 3%.

Richard Hunter, head of UK equities at Hargreaves Lansdown Stockbrokers, said the figures “underline the continuing polarisation of the UK banking sector”.

“The continuing spectre of Government interference looms over the likes of Lloyds and RBS, whilst Barclays and HSBC remain free of such shackles,” he added.