Greater Anglia say all but two of their rural routes will be operating a normal service on Monday.
The train operator has been plagued by issues with their new trains and the network's signalling systems.
It has resulted in severe disruption to local routes in Norfolk and Suffolk over the past two weeks.
In a joint statement on Friday, 13 December, Greater Anglia and Network Rail said they are still carrying out tests on what has caused the issues.
"Today we have been able to put in more services and from Monday we aim to restore a full service on all routes except Norwich to Sheringham and Ipswich to Peterborough.
Two routes will not have a full service on Monday:
There will be no trains between Ipswich and Peterborough.
There will be a bus replacement service between Cromer and Sheringham, though trains will run at a normal frequency between Cromer and Norwich.