So I'm seeing this girl at work in kind of a casual relationship although there's a bit more there than just a completely no strings attached relationship.
Problem is she has a boyfriend outside of work and because it's work we don't really want to let anyone know.
However, there's one other guy at work who seems desperate to get her attention, ie whenever there's a social event he's offering to walk her home or to the bus stop, hanging around and he's very pushy.
Kind of an awkward situation as by doing anything I let on that there's something happening and by not doing anything this guy keeps acting as a block.

try not fucking someones girlfriend.

This coming from you is a bit rich!
Now for the actual question...

Why is it a bit rich coming from Phil?

Morals aside - you're asking how to stop somebody doing what your doing...

Either she has to tell him to back off or you have to take it like a man. It sounds less of a case of protecting your fb and more like protecting your own ego

Maybe you should ask yourself, is your self esteem that low tht you're willing to share with another man?

Either
1 it's casual no strings - ie you don't own her and can make no demands, enjoy if that's what you both want
2 she's going out with you, in which case suggesting she doesn't fuck someone else seems appropriate
As always meet more women and create other opportunities