The supporting headline says it all, the Charter of Fundamental Rights of the EU highlight rights that are already (mostly) present within the European Convention on Human Rights to which we ARE a signatory of. The Human Rights Act 1998 allow us now to argue the Convention rights within domestic courts.
No, the UK should not adopt a Charter of Fundamental Rights like the rest of the EU, because the UK did not become stronger than the rest of Europe by following its example. A charter of fundamental rights opens the UK up to obligations and liabilities that it might not be able to afford. It should not adopt such a charter.
While most of the principles stated in the Charter of Fundamental Rights appear agreeable, adopting it under the current structure of the European Union is a massive mistake. That is because in practice it empowers unelected and unaccountable EU judges to interpret the document as they see fit and impose their will over the national laws and the democratically elected parliaments of sovereign nations. In this way, adopting the Charter would actually be a violation of fundamental rights.