Banks that use Travelex to run their foreign exchange services are still unable to sell travel money after a massive cyber-attack which happened two weeks ago.
Hackers held Travelex to ransom, demanding the firm pay $6m (£4.6m) before they unlock its systems.
That has affected banks like Barclays, Lloyds and RBS, which use Travelex to provide their travel money services.
And Travelex has refused to say when some services will be restored.
In a statement, the foreign exchange firm said it is making "good progress" recovering its systems.
The firm is hoping that employees in its stores, who have resorted to using pen and paper since the hack, will be able to switch on their computers again by the end of this week.
But its website, which was taken down immediately after the attack was launched two weeks ago, is still offline.
Travelex has not said when it will be back up and running.
Banks that depend on its foreign exchange services are still unable to sell travel money online or in store as a result of the attack.
Travelex was unable to say when all the services would be restored, although at least one of the banks was hopeful that it could be as soon as this week.
"We continue to make good progress with our recovery and have already completed a considerable amount in the background," said Travelex boss Tony D'Souza.
"We are now at the point where we are able to start restoring functionality in our partner and customer services, and will be giving our partners additional detail on what that will look like during the course of this week," he said, without specifying when systems would be restored.
The firm said: "There is no evidence to suggest that customer data has been compromised."
However, the hackers, a gang called Sodinokibi, have told the BBC they gained access to the company's computer network six months ago and claim to have downloaded 5GB of sensitive customer data.
Dates of birth, credit card information and national insurance numbers are all in their possession, they said.
Travelex said it is working closely with the Metropolitan Police, which is leading the investigation into the attack.