Your passport should be valid for the proposed duration of your stay; you don’t need any additional period of validity on your passport beyond this.
The Danish authorities have confirmed they will accept British passports extended by 12 months by British Embassies and Consulates under additional measures put in place in mid-2014.
You don’t need a visa to enter Denmark. As a British passport holder you can stay as a visitor for up to 3 months. For longer stays, you should apply for a residence permit.
Greenland and the Faroes aren’t members of the European Union. You don’t need a visa to enter for tourism, but you should get a work and residence permit before entry if you intend to live and work there.
UK Emergency Travel Documents
UK Emergency Travel Documents are accepted for entry, airside transit and exit from Denmark.