The line last month told agents they would be able to start placing fully refundable £400 deposits on behalf of their clients from 2pm on Wednesday. Priority booking access was also open to direct customers.
However, by 2.30pm, a message on the Celebrity River Cruises website read: "Due to unprecedented demand, our priority booking access is now closed." A spokesperson for the line confirmed to TTG that such was the demand, it closed access after six minutes.