I have a problem using the standard web links web part. The 'new and
organize' web part interface at the top is missing so I can not
add/change my links.

I am logged on as a user who is a co-ordinator. This problem has
only just occured, the web part interface used to be there. This
problem is the same for all web-links on my site.

I have tried deleting the individual web parts and adding them
again, but that made no difference.