BBC Radio 4's World at One programme has been given access to previously unseen letters to and from Downing Street, as well as cabinet minutes addressing the disaster in which 96 fans died in April 1989 following a crush at an FA Cup semi-final.
The Taylor Report, published following an official inquiry into the tragedy, concluded that the Hillsborough disaster was caused by a failure in crowd control by South Yorkshire Police.
However, the BBC has now revealed that Merseyside Police told the Prime Minister at the time that Liverpool fans were responsible.
In a letter written by a member of Thatcher's policy unit to the Prime Minister following a meeting with the late Sir Kenneth Oxford, it is said that the chief constable of Merseyside Police claimed: "A key factor in causing the disaster was the fact that large numbers of Liverpool fans had turned up without tickets.
"This was getting lost sight of in attempts to blame the police, the football authorities, etc."
Thatcher was also told in the letter from the advisor that an unnamed officer "born and bred in Liverpool, said that he was deeply ashamed to say that it was drunken Liverpool fans who had caused this disaster, just as they had caused the deaths at Heysel".
The stigma of guilt was quickly attached to Liverpool fans - not least due to the infamous coverage of the disaster by The Sun - but the Taylor Report made clear it was South Yorkshire Police and their failure to adequately control the crowd that were to blame.
In response to Thursday's revelations, Sheila Coleman, from the Hillsborough Justice Campaign, told the BBC: "We are really concerned that the emphasis is totally on Merseyside Police here and not on South Yorkshire Police, and that makes us very suspicious of how this information was leaked.
"We find it a strange coincidence that this information was leaked only days after we found out the [Hillsborough Independent] panel are not going to report until the autumn."
Margaret Aspinall of the Hillsborough Families Support Group, who lost her son James in the disaster, said comments made by the unnamed officer were "appalling".
"We knew things were going on behind closed doors, we've always known that," she added. "It doesn't surprise me in a sense... but I'm surprised by the content."
Documents relating to the disaster are currently being examined by the Hillsborough Independent Panel but are not expected to be released to families of the deceased until later this year.