The short answer is – nothing.
EU rules on free movement will continue to apply during a transition period, at least until the end of 2020. If you are legally residing in Denmark at the end of the transition period, your rights as a British citizen to social benefits remain unchanged as if you were still an EU citizen.
This also applies to future events. If, for instance, you become unemployed after the end of the transition period, your right to social assistance or unemployment benefits will be the same as that of EU citizens. You will also be able in the future to return to UK with your pension entitlements.
This home page will be updated with relevant links etc. In the meantime, you can take a look at the Q&As provided by the European Commission