you tell that you have a degree from a british university. To being eligible for unemployment benefits according to the special rule for graduates it is not a requirement that the program must be carried out in Denmark. BUT you must meet these conditions:
-You had a permanent address in Denmark no later than one day before the start of your education. If the applicant does not meet this requirement, it is possible to get unemployment benefits on the basis of a Danish superstructure (master, pHd etc.).
-You are in Denmark no later than 14 days (including weekends) after you end your education, i.e. you must apply for membership within two weeks (14 days) of completing your education.
It seems for me that you dont meet these requirements, but you dont tell if you were in Denmark before starting study.
If thats right, then you must follow the normal rules regarding unemployment benefits for earners. If you have contributed to Unemployment insurance fond (A-kasse) in UK, you can - as an EU citizen - transfer periods of employment and unemployment insurance between EEA countries.
Even though the UK has decided to leave the EU (Brexit) this will take some years. So as long as all the law about the brexit is not carried out, you will be an EU-citizen with the normal rights as other EU-citizens.