I am a Filipino citizen and I just received my Class-C Business Visa from the United Kingdom. My question is, as my company also has an office in Hungary, would I still need to apply for a Business Visa to enter the Schengen Area, more specifically Hungary?
As @DumpCoder already said in the comments, you will need a Schengen visa to visit Hungary. Having a Uk Business Visa could be helpfull for the Schengen visa application, but you will still need a separate visa.
The company office in Hungary is irrelevant, rent-a-car companies have offices all around the world, but having a visa for one of them will not allow you to visit all other countries.