The £200m scheme will provide a 1.6-mile link road between Junction 1 of the M54 and Junction 11 of the M6.
BAM had originally expected to start in 2022 but work was delayed by then transport secretary Grant Shapps to explore further environmental considerations.
The revised start date for this year will now be missed.
The roads agency announced last October that it was pausing early preparation work on the scheme to allow time for further detailed designs.
In a statement yesterday, National Highways said: “Since then, we’ve been carrying out assessments so the building of the scheme has as little impact as possible on the local community and environment.
“As a result of these assessments, we’ve reviewed how we’ll work with our supply chain to build this scheme.
“Consequently, BAM Nuttall’s involvement in this project will come to an end.
“We’re working with our supply chain to identify a new delivery partner for the scheme and we’ll set out when construction will start as soon as possible after that.”
It added that it remained committed to building the link road.
