JD Sports, which was tipped to rescue the 242-year-old department store, said was no longer interested after Arcadia, which is worth £75million a year to Debenhams, collapsed.
A notice on Tuesday night told shoppers attempting to get on the website: "You are in a virtual queue.
"Sorry for the wait, we are currently using a virtual queue due to exceptional demand.
"We will get you onto the site as soon as possible.
"Thank you for your patience.”
Some customers complained that the website crashed completely while they were in the virtual queue when reached the checkout page.
All of Debenhams' 124 UK stores are set to close following its collapse.
This means all 12,000 employees likely stand to to lose their jobs when the shops cease trading, unless administrators strike an agreement for all of parts of the business.
