Applying to theoretical physics Masters in Europe while not having a physics undergraduate degree I intend to apply to European Master programs in theoretical physics. I don't have an undergraduate degree in physics. 

My question is : Is an undergrad degree in physics absolutely required for admission ? Can I get admitted if I can demonstrate that I have the requisite background knowledge in physics and math ?

All the programs that I looked at explicitly state that an undergraduate degree in physics is a prerequisite for admission. 

I took the physics GRE test , teached college level physics "TA" , worked as a research assistant in theoretical physics , attended graduate level courses , can provide letters of recommendations. However , my undergraduate degree is not in physics.
This is a tough case. In many European universities, the expectation for master's study in a given discipline is a bachelor's degree in that discipline. Whether or not it is possible to petition for admission with another degree is up to the regulations of the particular university. However, if you do not have formal coursework available demonstrating that you have the requisite background, it is unlikely that you will be able to get approval. 

Your best bet might be to look for programs that are interdisciplinary in nature, as they tend not to have such stringent requirements.