Are there any legal requirements (H&S Env. Statutory inspection requirements) that a company can transfer to their contractors. OR will they be held jointly responsible should something go wrong.

They will be held jointly responsible. Although jointly isn't the same as equally. It will entirely depend upon the situation, competence of both parties, size of both parties, due diligence in advance and a whole host of other factors.

There are some exceptions WEEE springs to mind, but as a rule you cannot transfer liability to another person or organisation. Sometimes a joint liability may arise but that all depends on the actual circumstances. Very often the PC will be held responsible for actions of their sub-contractors, but again, it does depend on the material facts of the incident. Just as well you cannot transfer liability as it would be a right old merry go round! The HSE have stated there is no need to closely supervise sub-contractors. If you have selected competent contractors in the first instance, provided all the necessary information and support then there should be little to concern yourself...or, interpret it as you wish.