Can you run two businesses in one company?

Yes. A company can conduct any number of businesses under one company. If you want the different businesses to have different identities you will need different trading names.

There are only a few conditions to doing this. The trading names must not use certain probited words and acronyms that denote legal entities (Limited, Ltd, LLP, plc etc). Customers and suppliers must know the identity of the legal entity they are doing business with. This is usually achieved by putting the legal name in small print on the letterhead,websites and other marketing material.