The family of murdered private investigator Daniel Morgan say Home Secretary Theresa May has offered an investigation into police failings.
However, the family said they were disappointed after meeting Mrs May because they wanted a judicial inquiry.
Mr Morgan, 37, originally from Monmouthshire, was found with an axe in his head in a south London pub car park in 1987 but nobody has been convicted.
It is understood the home secretary has not ruled out a judge-led inquiry.
Four men were charged in 2008, but the case collapsed in March this year.
Mr Morgan's brother Alastair and other family members had an hour-long meeting with Mrs May, the first holder of her office to meet them.
The family want an examination of why the trial of three men charged with Mr Morgan's murder collapsed.
Speaking outside the Home Office, Alastair Morgan said: "The home secretary was proposing a police investigation into the cover-ups, if you like, and our position is that we want... no more police.
"We have had police for 25 years and they have done nothing for us."
He added: "It was profoundly unsatisfactory and we will be exploring all of the legal options to challenge the home secretary's position on this."
Mr Morgan said the family "immediately registered our total opposition of it and if there is any such inquiry it will not have our support".
A Home Office spokesperson said: "It is deeply regrettable that Daniel Morgan's killers have not been brought to justice and we understand the strength of feeling this case has caused.
"The Metropolitan Police and the Crown Prosecution Service are currently conducting internal investigations into the case and we expect their findings shortly."
The murder outside the Golden Lion pub in Sydenham has been investigated five times, including bugging suspects' offices and homes.
Mr Morgan's family have fought for many years for action - making allegations that investigations have been affected by police corruption - and say the case is "crying out" for a judicial inquiry.
Before the meeting, Alastair Morgan said: "We have been writing to them [the Home Office] about the case for two decades or more expressing fears of corruption etc.
"I want this judicial inquiry because I want the public to see exactly how our police investigate the most serious allegations of police corruption."
The Metropolitan Police now admit "police corruption was a debilitating factor" in the first investigation in 1987 and have apologised to Mr Morgan's family.
His mother Isobel Hulsmann, 83, from Hay-on-Wye, Powys, travelled to London last month to try to see Mrs May and push her for a judicial inquiry.
The minister was unable to see her on that occasion but a meeting was agreed.
Lawyers acting for the family previously sent Mrs May a submission setting out the grounds for a judicial inquiry.
Politicians, including Brecon and Radnorshire MP Roger Williams, have backed the campaign.