I can't take credit for this as Rose support found it for me - I have run through these steps and it worked ( I skipped step 1 as the script didn't look like it would have made any changes to the table. It was written for GP10.0 but worked fine for GP2013...
Note Before you follow the instructions in this article, make sure that you have a complete backup copy of the database that you can restore if a problem occurs.
1. Follow the steps in the following Microsoft Knowledge Base article:
849988 Cannot create a new or old fiscal period, primary key constraint SY40100
2. On the Microsoft Dynamics GP menu, point to Tools, point to Setup, point to Posting, and then click Audit Trail Codes. In the Audit Trail Codes Setup window, print the information for reference.
3. On the Microsoft Dynamics GP menu, point to Maintenance, and then click Clear Data. In the Series list, clickCompany, click Audit Trail Codes, click Insert, and then click OK.
4. On the Microsoft Dynamics GP menu, point to Tools, point to Setup, point to Posting, and then click Audit Trail Codes. Select the Next Number column for each origin and prefix. Then, reenter the next number from the information that you printed in step 2. If two origins have the same prefix, insert the larger next number.
Note In the Audit Trail Codes report that you printed, you may see more origins than you see in the Audit Trail Codes window. The additional origins that you see are not required, and you do not have to add them.
5. On the Microsoft Dynamics GP menu, point to Tools, point to Setup, point to Company, and then click Fiscal Periods. Then, set up your new fiscal year.