I'm from a country that is part of the European Union (EU), do I need to apply for the HSMP or Points Based Visa?

In most cases, no. As a citizen of a nation that's a member of the EU, you are entitled to settle anywhere in the European Union, including immigrating to the UK. You are allowed to live and work unrestricted and do not need to apply for HSMP. They will also not have to apply to immigrate to England under the new UK Points Based Immigration System. There are no restrictions on the types of jobs you can get or the places you can live. Consider yourself lucky if you are an EU citizen and want to move to the UK, the process of UK immigration in much easier and you certainly won't need an UK immigration lawer.