Can I make a claim against my employer while I am still working there?

This is always a difficult question, and one that is hard to answer as a blanket statement.

If you are still employed and wish to keep working there except for the current situation, then attempting to solve the problem through any sort of internal HR mechanism may be the easiest way to go. HR may be able to find a workable solution that can diffuse any tensions. If however HR is unable to assist, then speak with an employment lawyer to see what your options are. Depending on your specific case there may be a way to resolve things peacefully without disrupting your employment.

Otherwise, if the problem is serious or one that persists, you may want to reassess whether that workplace is a healthy one for you. If your employer has created a toxic or poisoned workplace with their conduct (as noted above), then there may be an option to pursue a legal remedy that may also involve you leaving your workplace, so it is one to discuss thoroughly with your lawyer before taking any steps.