Emergency full-time marking centres have been set up so examiners can work seven days a week to mark national tests taken by 11- and 14-year-olds.
Two "marker panels" have been established in Leeds and Cheadle, near Manchester, where examiners are working eight-hour days to get the scripts marked.
Examiners were supposed to have finished all the marking by Monday for the key stage 3 tests, and by yesterday for KS2.
But the National Assessment Agency (NAA) told The TES that more than a million of the papers were not listed as being marked on its systems on Monday. The revelations will place fresh pressure on ETS Europe, the American firm running the marking operation for the first time this year, amid complaints from scores of examiners that the administration has been a shambles.
More than 300 examiners have complained to the NAA about their experiences. Problems range from disorganised training to computer glitches and emails and phone calls not being returned.
Some markers were this week still waiting for papers to be collected from their homes, which they were unable to mark because the ETS computer system said they were not supposed to be marking them.
Some markers have been sent scripts for the wrong key stage. One teacher allowed The TES into her home to see her three unopened boxes of scripts, athough she feels unable to contact the schools involved and cannot be named because all markers have signed confidentiality contracts.
The KS2 maths marker received the boxes of KS3 science papers last Friday, completed by pupils at four schools. The boxes were still sitting in her kitchen this week because, she said, ETS had not replied to emails from her asking for them to be collected.
The marker said: "Pupils and teachers are all eagerly awaiting their impending results. Little do they know the papers are sitting in my house."
A KS3 maths marking supervisor said this week that all eight of her marking team had experienced technical problems in finishing their marking allocation.
The marking panels cover both key stages and all subjects, although backlogs are most urgent in KS3 English.
The Cheadle marking centre opened on May 21, while the one in Leeds began last Saturday.
The NAA said more than 85 per cent of scripts - or 8.2 million out of a total of 9.5 million - had already been marked. Many of the others, it said, had yet to be formally registered as marked.
It said 77,000 scripts had been marked by the panels in the two centres so far, with another 23,000 due to be marked by July 1.
About 150 markers are working on the panels. Most of them are senior examiners, although not all of them had worked as teachers before.
Teachers on the TES online staffroom are furious that markers on the panels are being paid at least pound;180 a day, when others have been waiting for weeks for scripts and are not being offered the work.
The NAA said it remained confident that all results would be issued to schools by the target date of July 8.