For stays of up to 3 months your passport should be valid for the proposed duration of your stay; you do not 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.
Visas are not required 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 are not members of the European Union. Visas are not required for tourist purposes, but you should get a work and residence permit before entry if you are intending to live and work there.
UK Emergency Travel Documents
UK Emergency Travel Documents are accepted for entry, airside transit and exit from Denmark.