Most of the money for the first round of Olympics tickets sales will be debited from applicants' bank accounts by next week, organisers have said.
Locog said 60% of cards would be debited by midnight on Wednesday, the "vast majority" by 31 May, and the process completed by 10 June.
The process had been due to begin on 10 May, but cards did not start being debited until at least a week later.
A different system is to be used for the second round of ticket sales.
The current system has attracted criticism from various quarters - including from consumer group Which? - for taking the cash from applicants' bank accounts before they know which tickets they have been allocated.
London 2012 organisers Locog say the system is fair.
The second round of sales, in late June, will initially offer unsuccessful first round ticket applicants the first chance to buy those tickets still available, said the organising committee.
It will take place on a 'first come, first served' basis with the money paid up front.
The general public will later be able to apply for remaining tickets.
London 2012 chairman Sebastian Coe said they had always intended to have a different system for the second round.
First round applicants have been receiving e-mails from the London 2012 ticketing team to say they are now taking payment from Visa credit and debit cards, as well as banking cheques and postal orders.
The process is due to be complete by 10 June. Applicants will be contacted by 24 June to confirm if they have been successful in obtaining any of the 6.6 million tickets available and if so, which they have been allocated.
The e-mail said Visa payments would only be taken for successful applications, and that if cards had been lost or stolen, or there were any issues with collection of payment, applicants would be contacted about it by 10 June.
London Organising Committee of the Olympic and Paralympic Games (Locog) deputy chairman Keith Mills said they were trying to make sure the system was "fair and even" and that people were informed at the same time about whether their application had been successful.
He told BBC Radio 5 Live: "One of the problems when you are doing something on this scale is if you tell one person they've got tickets, they tell their friends and suddenly we have a switchboard jammed with people - so we are trying to do this extremely thoroughly."
"It's going brilliantly well - it's very complex, but it is going brilliantly well," he added.
He added that hundreds of thousands of unsold tickets would be available to buy later in the year.
London 2012 organisers recently revealed that there had been more than one million requests for tickets for the Olympic men's 100 metres final, on 5 August next year.
They are looking to make £500m from ticket sales as part of bid to raise £2bn through private means.
The price of Olympics tickets ranges from £20 to £725 for the showpiece 100 metres final, and reaches £2,012 for the opening ceremony on 27 July.