What is the relationship between SC and EU?

There were two famous cases that established that EU law was superior to UK law. One of these was the Factortame case in 1991. It ruled that the 1988 Merchant Shipping Act that limited the rights of foreign ships to fish in British waters contravened EU law.
The EU therefore ruled that the foreign vessels could now fish in these waters. This showed that the judiciary now had to enforce EU law and that the European Court of Justice will always have the final say if there is any dispute.

The European Court of Human Rights that was set up by the Council of Europe allows citizens who believe they have had their rights abused by the government, and if they believe that the British Court has not interpreted the HRA correctly, the right to appeal to them.
If it finds the Convention has been broken it can reverse the decision in question. This is the highest appeal so a case can go no further.
There is however an exception, and that is that the ECHR cannot set aside any law made by the Westminster Parliament as this is not subject to the European Convention.