Web sites do not have their own laws, they fall under long time laws covering Media. A general rule of thumb is that if you can get consent, they should. I used to be webmaster for the Capitols newspaper. The web site and the paper came under the same laws. If the picture is of someone/people who are center objects, they need to agree.
If they are background and happened to be caught... then you generally don't know it and consent is not required. Imagine a sports photographer having to track and ask every person in the bleachers...
So the basic rule of thumb is that if they are the subject they need to agree, if they are more background noise they do not.
This case however is different in that it sounds like they are employees. I cannot say what law would cover that... they are working on his behalf, it is the company web site so they may not have a say in it. A good boss would ask if anyone has an issue of that person is the target/focus of the photo.
I done a school website and government web sites of employees where people did not want their image online. So that should be respected and not used. But as web designer that is not your call, that should be handled by the employer/owner.
My wife did photography for the paper. she always asked first and once in a while someone would decline, but rarely. Another freelance photographer got in allot of trouble for photographing kids at a Santa thing and not telling anyone why. he did not identify himself to anyone, and we had to jerk all the images offline to avoid problems when the organizer saw the kids online without permission from them or the parents.