The Council of Europe is Europe's human rights supranational organization. Its basic treaty is the European Convention on Human Rights, which is distinct from the Charter of Fundamental Rights or the European Union. Blair's greatest achievement as Prime Minister will probably end up being the adoption of the Human Rights Act 1998, which he ironically spent considerable energy trying to undermine in the second half of his tenure just like he tried to undermine the EU's own Charter of Fundamental Rights. The Council of Europe created the European flag and allowed its use by other European institutions. The only country West of the Urals, and north of the caucasus not in the Council of Europe is Belarus.
The European Council or Council of the European Union is the EU institution representing the governments of the EU member states. We have met the enemy, and he is us — Pogo