It depends a lot on what you have there.
If something is very prestigious, it should be known to those reading your CV without you adding footnotes.
If you worked for very well-known institutions and now add footnotes or similar explanations, you risk coming across as patronizing. Your readers may think you are taking them for idiots. Normally, people with several years in any industry know its main institutions, schools and similar. Just as everyone is Europe has heard of Harvard, most educated people in the US have heard about Cambridge.
On the other hand, if you're applying in a different field, unrelated to your prestigious work history, then the fact your past employers were prestigious probably won't impress anybody. Adding footnotes might make you come across as delusional, stressing something meaningless in the field you are applying in.
You might add a short explanation next to the institution, but should check twice whether the two risks described above aren't valid in your case. If you chose to do so, only add very short, objective assessments (e.g. by adding some source of your claim) without referring to the institutions as being prestigious or considered the best. Make it as fact-based as possible.