Mowlem refused to carry out the work to discover the source of a leak. The architect said the problem was poor workmanship, the builder says it was poor design.
Symonds will now carry out an audit of building and then complete the project using specialist contractors.
The council said Mowlem's contract is at an end and has instructed them to leave the site.
The project was first hit with peeling paint problems in August 2003 and the council said that since then it has 'struggled to keep Mowlem committed to completing the project.'
In a statement the council claimed it has had to work through the architect and contract administrator Nicholas Grimshaw as the architect and builder blamed each other for a host of problems.
NESC project manager John Betty said 'The problems which hit the headlines - peeling paint and leaking floors - are not the only issues we have had with Mowlem,'
Mowlem was not immediately available for comment.