To be late to work means to arrive late at work or to be late for work (probably the last of these is a more common expression). To "be to work late" is not quite correct. You can say "to get to work late" which means the same as "to arrive at work late". However, the title of your question says "to work late..." This is different. If I am "working late", or if I say that I'm going to "work late", it would normally mean I am staying at work later than usual and I won't be coming home at the normal hour. Just to confuse things, you might also say "I'm going to work late this morning", which would more likely mean I am going to arrive at work later than usual this morning.

i think is 'Be late to work','be late to' is a phrase