In determining whether the European Union has undermined the United Kingdom's sovereignty, one would need to have a decent definition of sovereignty.
1) If any action by the EU trespasses on this definition, then the answer must be yes. If not, then no.
3) Does the EU restrict the work of the Lords?
4) Does the EU restrict the work of the Law Lords + judicial system?
5) Does the EU drive government policy?
6) Are manifesto promises/pledges made with one eye on the EU?
7) Do the EU courts impact the UK?
8) Does the Euro impact the UK?
9) Is the UK becoming more European as a result of the EU?