Scotland Yard has asked the Government for £38 million towards the Grenfell Tower investigation, claiming the demands on police time could leave them facing unreasonable costs.
Around 200 officers from the Metropolitan Police are continuing working on the criminal probe into the fire, which killed 71 last June.
The force has made a request to the Home Office to fully fund the £27 million cost of the inquiry in the coming financial year, their finance chief said on Thursday.
A further £11.1 million is also being sought to cover extra hours put in by investigators so far.
Under current rules, a police force can apply for a special grant to help foot the bill of an investigation once it exceeds 1% of their budget.
Given how many officers Scotland Yard faces committing to the Grenfell Tower investigation for a second year, it has asked the Home Office to go further.
The London Assembly's budget and performance committee was told the department had provided assurances their request was being given "serious consideration".
Lynda McMullan, the Met Police's director of finance, told the hearing the Grenfell disaster "has had a very significant impact and we've put in a special grant claim for the current year for £11.1 million".
She said the Met estimate that it will be spending close to £27 million on the Grenfell investigation.
"We are asking whether or not we can have dispensation, not just simply the 1% referenced, but we also want to claim the full cost of our officer time for that investigation."
She added: "We don't think it would be reasonable for us to pick up the full costs, as we know that investigation will go on for some time."
Home Office officials have told the force that the matter will be put to ministers, who will decide whether to wave through the additional funding, the committee heard.
The size of the Grenfell Tower probe has previously been described as "unprecedented", involving many months of evidence removal from the west London block, as well as the seizure of millions of documents.
Offences, including misconduct in public office, manslaughter, corporate manslaughter and breaches of fire safety regulations are being examined by detectives.
Suspects are not expected to be interviewed until later this year in relation to the disaster, while Scotland Yard expects to hand the tower - still a crime scene - back to Kensington and Chelsea Council in the spring.
Ms McMullan continued: "We would like to have full costs rather than incremental costs for the next year because of the fact given, after a reduction in the number of officers, it doesn't seem reasonable we would absorb that full cost of those 200 officers.
"We have got assurances it is being serious consideration."