Government ministers and the NHS ignored warnings about persistently high death rates in hospitals which could have claimed the lives of up to 20,000 patients, a top health adviser has said.

Professor Sir Brian Jarman, who co-founded the health statistics and research service Doctor Foster, said he had sent the then health secretary Andy Burnham a list of hospitals with higher-than-average death rates in 2010, but no action was taken. Several of those hospitals are now the subject of a Government review into their high mortality ratios.

Mr Burnham, the MP for Leigh, has rejected Sir Brian's claims that his warnings were ignored and said he did act to uncover failings in care. Sir Brian's comments come after the publication of the highly critical Francis report into poor care at Stafford Hospital which identified "failings" across the NHS and recommended reforms of the health system.

Sir Brian said statistics showed that for a decade four hospitals had hospital standardised mortality ratios (HSMR) - which gives a figure for whether death rates are higher or lower than would be normally expected - which were "continuously very high".

He sent an email about those findings to Mr Burnham, who responded saying by passing that information to the hospitals' watchdog the Care and Quality Commission (CQC), but they took no action. Mr Burnham said he acted "firmly and immediately" by referring the data to CQC, and by later commissioning the first inquiry carried out by Robert Francis QC into Stafford Hospital, in 2010, which uncovered "shocking" levels of care.

Sir Brian, a former president of the British Medical Association, is working on a Government review of 14 hospitals where mortality rates have been persistently higher than the national average.

Speaking on BBC's Today programme on Radio 4, he said: "For the last 10 years there were about four (hospitals) who have had continuously very high adjusted death rates. Actually I sent to the Secretary of State in March 2010, Andy Burnham, a list of hospitals which had high mortality rates and there are seven of the ones on the list that have just been mentioned."

Mr Burnham replied to him but said the CQC "did not find that there was anything to worry them". "I think that it's a pity they didn't because you have seen at Mid Staffs and we've seen at other hospitals that when they have actually gone in and looked they have been able to reduce the death rates. We are talking about people dying there."

Sir Brian said, referring to data from the 14 hospital trusts identified as having high HSMRs, that "observed deaths exceeds the number they were expected to have by the national average". He estimated the deaths at these trusts alone could have amounted to "a bit over 20,000".

Mr Burnham, who was health secretary in the former Labour government, told the Today programme: "I have great respect for the work carried out by Sir Brian but the claim that ministers and civil servants ignored his warnings are not true." He rejected claims he was complacent at the time, adding he invited Sir Brian onto a working party following the publication of the first Francis report. Mr Burnham said during that period HSMR data was "new" and "the Government could not put it's full weight behind it".