The European Convention on Human Rights (which set up the court) ensures that the citizens of all signatory states are afforded certain universal truths and values. As a signatory of this (as a member of The Council of Europe -
NOT the EU) we must ensure this is true when dishing out legal remedies. This means that we are duty bound to ensure that any decision that is taken by British Courts complies with the values set out by the convention.
I suppose that's one reason why the ECHR hasn't been sought in the Mckinnon case as it's questionable if his conditions will be any worse than he would experience here. Though, if his medical conditions are true then I do not suspect that the ECHR will authorize his extradition.
I can type out the things which the ECHR sets out if you wish but you should be able to find it with a quick google but I appreciate law texts aren't awfully fun to read (and that's coming from a law student!)
Read the Treaty on the Functioning of the European Union, article 20.