The short answer is no.
Not only do the active ingredients have to be fully tested and passed by the MHRCA, but they also have to approve the manufacture of the product. So a company will receive a licence to manufacture a specific product, which covers the full formula. If they then choose to supply the product to a third party, this is only a licence variation and does not require any testing.
However any subsequent change to that licence however minor has to be approved by MHRCA and so if the holder of the PL wants to change say the supplier of an active ingredient it may have to undergo a new testing regime.
Animal testing and the nuances of the wording used by manufacturers isa very difficult area, you should direct your questions directly to the company concerned.