Do I need to move the HQ of my company?

Hi,

I have a company registered in my country and would like to keep the Headquarters of my company in my country doe to low taxes.

I would like to move to the UK with my family and set up a UK subsidiary of my company in the UK on Tier 1 Entrepreneur visa. Can I get a Tier 1 Entrepreneur visa if I don't relocate my headquarters?

In order to come here and eventually extend your stay, you need to register a company here in the UK and pay UK taxes (income tax, corporation tax, business rate, VAT, etc) This company can indeed be a subsidiary of your current business at home but ANY tax applicable with respect to this subsidiary and its generated revenues have to be legally paid here.