The law on Dual Nationality came into force on 1st September 2015.
The law means that Danish nationals who wish to acquire a foreign nationality may do so without losing their Danish citizenship. In this regard you do not need to take any action in relation to the Danish authorities. If, for example, you wish to apply for British nationality you must do so via British authorities:
Once you have British nationality in addition to your Danish nationality you have dual nationality. It may also be possible for you to apply for further nationalities. You will then have multiple nationality.
Please see the information on the website of the Danish Ministry of Immigration, Integration and Housing:
Furthermore, during a period of 5 years from 1st September 2015 to 31st August 2020 persons who have previously lost their Danish nationality will be able to apply to the Danish State Administration (Statsforvaltningen) to regain their lost nationality:
ansøgning ved erklæring (Danish only)
Use application form (4): Erklæring - tidligere danske statsborgere - uden bopælsbetingelser
Please note that if you have lost your Danish nationality because you did not fulfil the conditions of the 22-year rule, it is not possible to apply to regain it by Declaration: the 22-year rule
Your declaration including supporting documents should be sent direct to the Danish State Administration: Statsforvaltningen, Storetorv 10, DK-6200 Aabenraa, Denmark. The application fee of DKK 1.100 must be paid in advance direct to the Danish State Administration. Further information is available here.
You can, however, also submit the application through the Embassy or a Danish speaking Consulate/Vice-Consulate, but the following fees would apply (in addition to the application charge paid direct to the Danish State Administration):
£22.00 for the Embassy/Consulate/Vice-Consulate to receive, submit the application and forward the Certificate of Nationality to the applicant at the conclusion of the application. The application will not be checked. If you choose this method, further charges may apply, for example if it involves further correspondence with the Danish State Administration, see below:
£110.00 per hour or part thereof for the Embassy/Consulate/Vice-Consulate to undertake the whole application and any correspondence with the Danish State Administration.