William Stobie leaves Belfast crown court
Hugh Orde of the Metropolitan police said they hoped to report their findings early in the new year, but that the investigation was continuing.
Mr Finucane, a high-profile Catholic solicitor, was shot dead by the Ulster Defence Association in front of his family at his home in 1989.
On Monday, the only person to face trial over the murder walked free when the case against him collapsed.
In a statement, the Finucane family said both the Stevens Inquiry into RUC collusion and the William Stobie court case were a deliberate delaying tactic to obstruct a public inquiry.
Evidence
Lord Chief Justice Sir Robert Carswell returned a verdict of not guilty in the absence of evidence against Stobie on Monday.
It followed a ruling that former journalist Neil Mulholland - the main prosecution witness - was incapable of giving evidence.
The self-confessed ex-Ulster Defence Association (UDA) quartermaster and one-time RUC informer was accused of aiding and abetting in the murder of Mr Finucane in February 1989 and in the murder of student Adam Lambert.
The UDA is the largest loyalist paramilitary group in Northern Ireland.
The collapse of the case also meant a not guilty verdict being returned on Mr Stobie over Mr Lambert's murder.
The Protestant student was shot dead by loyalist gunmen who mistook him for a Catholic when he was working on a north Belfast building site in 1987.
Mr Mulholland interviewed Mr Stobie in the early 1990s.
'Not giving up
Mr Orde, the Metropolitan Police's deputy assistant commissioner, said his team had not given up.
Speaking on BBC radio on Tuesday, he said: "We are here to investigate this crime to the best of our professional ability.
"We will comply with all the rules of law and we will not step outside the rules of law to investigate that crime.
"But we have not gone away, and whilst I am not optimistic quite frankly at the moment, we have not given up."
SDLP justice spokesperson and assembly member Alex Attwood said Mr Orde's comments on behalf of the Stevens inquiry could prove to be helpful.
"His confirmation that there were no significant pending criminal prosecutions and consequently no impediment would arise in respect of the international judge investigating the Finucane murder, now enables the appointment of the judge and the work of the judge to commence without delay," he said.
After the brief hearing on Monday, Stobie said: "I am glad it's all over."
Stobie is considering legal proceedings.
'Vindicated'
Meanwhile, a judge of international standing is expected to begin a fresh investigation into Mr Finucane's murder by next April.
The appointment of a judge was agreed at the Weston Park peace process talks.
But the Finucane family said it was not enough and are calling for a full public inquiry.
Mr Finucane's son, Michael, said he believed there was never any hope of a successful criminal prosecution.
He said the British Government could "not duck its responsibilities" and must implement a full independent judicial inquiry into the killing.