Who in a small business can sign an employment contract?
There are no special rules for employment contracts; the same rules apply as with any contract.
Company directors will usually have the authority to sign employment contracts on behalf of the company.
Others may be granted the authority to sign, although it is (according to an employment lawyer friend) not uncommon for junior HR staff to sign without any thought as to the question of authority.
For more information about authority and the execution of documents, see this article from Shoosmiths: