Are European Union member states compelled by law to implement EU directives and regulations, or can they choose not to implement them for any reason?
The meaning of "regulations" and "directives" are specified in Article 288 of the Treaty on the Functioning of the European Union, which reads (emphasis mine):
To exercise the Union's competences, the institutions shall adopt regulations, directives, decisions, recommendations and opinions.
A regulation shall have general application. It shall be binding in its entirety and directly applicable in all Member States.
A directive shall be binding, as to the result to be achieved, upon each Member State to which it is addressed, but shall leave to the national authorities the choice of form and methods.
A decision shall be binding in its entirety. A decision which specifies those to whom it is addressed shall be binding only on them.
Recommendations and opinions shall have no binding force.
So yes, the UK – or any other member of the EU – is bound by all the EU regulations and directives.
The EU commission publishes a yearly report to monitor the application of EU law during the preceding year. For the UK specifically you can look at the "scoreboard" for the country, and see that in general the UK complies with EU law, but that there are various infringement cases.
The member states are not exactly compelled by law, they committed themselves to do it by entering the EU treaties (the so-called “primary EU law” and the source of everything else).
The framework created by these treaties foresees two major ways in which EU law can be enforced and has a bit more “bite” than international law in general:
- EU law is binding on national courts, which can enforce it themselves. EU law has become a major source of law in the member states and local courts can also enforce it, against their own government if need be.
- Infringement proceedings in front of the EU Court of Justice. In a nutshell, the EU Commission or, in very rare cases, other member states, can bring an EU member state in front of the Court for failing to implement directives or correctly apply EU law. After a few more steps, the court can impose heavy fines and states almost always comply.
There was a related question: How much can an EU member delay implementing a directive in its national legislation?
It's September 2018 now, the UK is supposedly leaving the EU in March 2019, so if you look at the other question, there is no way in practice that the UK could be forced to implement any EU directive by March 2019.
Regulations are different. EU regulations are law in the UK until March 2019, without having to implement anything. On the other hand, the UK can choose to enforce or to not enforce laws, and any complaints about that would not achieve much in six months. Plus the EU would probably not try very hard to enforce things at this point in time.
Maybe someone knows about some EU directive that the UK is supposed to implement and doesn't bother.