Is that a Nimrod rack - looks similar though not identical to mine.
Pannier bags have different mechanisms for mounting on the rack - the bottom of the pile, its sort of velcro attachments. My first Dawes pannier bag had plastic clips which I pushed open individually to release, the ortlieb system and others like it make it easy to remove your pannier at your destination. The better systems have adjustable hooks to cope with the variation in racks, and allow the lower hook to be moved as well.
Are there any other cyclists at work - if so have a look at their panniers, and try mounting them on your rack.