Baroness Nuala O'Loan, who was Northern Ireland's first police ombudsman, said the issues must be dealt with separately.
She said victims were being held "to ransom" during the political stalemate.
"If you choose between the ability of people to get prosthetic limbs and welfare reform, that to me is totally morally wrong," she said.
Speaking on the BBC's Good Morning Ulster programme, she accused both the Westminster government and Stormont's devolved government of failing to play their part in resolving ongoing problems caused by the Troubles.
Baroness O'Loan said victims who had conflict-related injuries were not getting the financial support needed because of the budget row over welfare reform.
"We have people today who are suffering a great deal, we need resources and we need progress on the past in order to enable the present," she said.
The former police ombudsman also said ongoing sectarian violence was the result of failure to deal with Northern Ireland's troubled past.
"People can think that we're at peace, but we had three deaths last year, we had 94 shootings, we had 26 bombing incidents, 58 firearms recovered. We still have a state of conflict and we need to work as a society towards reconciliation.
"The British government need to play their part and our own government need to play their part and I don't think either are doing it at the moment."
Ulster Unionist leader Mike Nesbitt said Ms O'Loan's "argument" had "some merit".
"At the start of the Haass talks two years ago, I argued that we should steer well clear of this formula, and bank agreements as we progressed," he said.
"I made the same pitch at the start of the Stormont House process, sadly without success, and as a result, victims and survivors once again find themselves in limbo, listening to rumours of the possibility of real progress in service provision, but unaware of the real prospects for actual delivery, not least in the area of better mental health and wellbeing."
Mr Nesbitt said Ms O'Loan's intervention had come "hot on the heels" of speculation in a media briefing that the UK government was considering implementing singular aspects of the agreement.
"This all has the whiff of softening up the public for a side deal being brought forward over and above the heads of the five Executive parties," he said.
"Our concerns over side deals was one of the reasons the Ulster Unionist Party felt unable to fully support the Stormont House Agreement last December, and as time passes, the wisdom of that decision appears to strengthen by the day."
The Westminster government had agreed a number of new measures to address Troubles legacy issues during last December's Stormont House Agreement.
However, the deal has been in jeopardy since March, when Sinn FÃ©in withdrew its support after a row over how future welfare claims would be dealt with.

Detectives were ordered to re-examine thousands of accounts dating back to 1994 in light of the Rotherham scandal.
They found no evidence of "historic, systematic abuse" but have reopened five unconnected cases, the force said.
The review only included reports which are not linked to current investigations.
A team of experts looked at reports into 866 individuals to decide if they had been victims of sexual exploitation.
In cases where they had, they assessed whether the complaints had been properly investigated at the time.
This uncovered further names - a total of almost 7,000 - all of which were followed up.
Details of any potential victims were passed on to teams of detectives, who felt five cases warranted reopening.
The report concluded: "There is no evidence to suggest that any large scale systematic child sexual exploitation has been uncovered in Leicestershire".
Police and Crime Commissioner Sir Clive Loader, who ordered the report, known as Operation Sepia, said he was "reassured" by its findings.
Assistant Chief Constable Roger Bannister said he was satisfied the "comprehensive" review would have uncovered any evidence of systematic and organised abuse if it had existed.
But, he added, only records from Leicestershire had been examined, and called on victims to come forward if they felt their case had not been adequately investigated.
It is "immoral" for the government to refuse to deal with Troubles legacy problems unless welfare reform is agreed, a former watchdog has said.
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Five separate child sex abuse cases have been reopened by Leicestershire Police after a review of 20 years' worth of reports.