About 210 posts will go at Darlington and another 120 will be lost from Morecambe, the company said.
The cuts have been attacked by the Amicus union, which said it had not been consulted about the job losses.
The jobs will be transferred to sites in Norwich and Bristol.
"We are extremely disappointed at the cavalier approach Norwich Union has taken to the livelihoods of so many hardworking and loyal staff," said David Fleming, Amicus' national secretary.
"There has been no consultation and the staff at RAC are understandably shocked."
Norwich Union, owned by Aviva, bought RAC for £1.1bn in March this year, and with the purchase announced it would cut 1,700 posts - 900 from support divisions and 800 to be offshored.
Combining the two businesses would help it achieve cost savings of at least £80m a year by 2006, it said.
Meanwhile, the insurance company hopes to increase sales of financial services to the RAC's 6.7m customers.
Last week, Aviva announced half-year profits of £1.32bn and said the integration of RAC was progressing quickly.
As part of this process, Aviva said it had already marked another 380 roles that it believes can be removed across the two organisations, on top of the cuts announced.