There are relatively few formalities to consider when moving to Denmark from the UK. If you are an EU citizen, you just have to apply for an EU residence permit within 90 days of arriving in Denmark. You will need to present an employment contract or proof of your ability to finance your stay in Denmark or proof that you have a family relationship with a EU citizen living in Denmark. If you are a non-EU citizen, you have to apply for a residence permit before arriving in Denmark.
Customs & Import Restrictions
Although Britain is not a member of the Schengen area, and therefore customs formalities apply, because we are members of the EU, there is little of consequence to concern the average Briton relocating to Denmark.
There are no general import restrictions. Free import of goods bought from the EU with some restrictions on the amount of alcohol and cigarettes. Medicines for personal use only.
Generally speaking, if an item is allowed in the UK it is also allowed in Denmark. There are no restrictions on items such as obscene or pornographic objects and publications or other such items which may be prohibited in some countries.
If you bring with you excessive amounts of limited goods (i.e. alcohol or tobacco) when moving to Denmark from the UK, you should declare these at your point of entry. This can be done either in person or, more usually, by filing out a customs form upon arrival, as the customs offices are rarely staffed.
Be aware that notwithstanding the general limitations on alcohol and tobacco, it is only allowed to import these goods for personal use. If the goods are intended for re-sale, they should be declared no matter the amount. Also note, that the general limitations only apply to persons aged 18 or above. Persons aged 16 or 17 are not allowed to import spirits, fortified wines or tobacco, but they may bring with them the same amount of beer and wines as adults.
You will need a Civil Registration Number (CPR) from your local municipality. For this you must have a home in Demark, and a residence permit from the immigration authority. You can get this before you leave the UK but the CPR can only be obtained after your move, and you have to collect it in person. However, you have to live in Denmark for 5 years, three of them working in Denmark, before you can get a permanent residence permit. There are special rules for pensioners, and people with strong ties to Denmark. This website gives you up-to-date information: NyiDanmark. When you have your CPR number, you will automatically receive a health card.