You will find it hard to import a gun without a provable good reason for having a firearm, e.g. you are taking part in clay pigeon events.
There are two scenarios dependent on whether the shotgun is imported before you move to the UK or not, they are:
If you import before you are a resident in the United Kingdom (UK) then you will need to get a "British Visitors Firearms Permit" (BVP). In order to get a BVP you need to get a "Sponsor" who lives in the UK to apply on your behalf. The sponsor must apply to the Chief Officer of Police for the area that you will live in. Application forms are available from all local Police stations.
The sponsor should:
Fill in the application form on your behalf;
Give details of all events you will be taking part in; and
Send the firearms permit to the foreign importer (you) once it has been granted.
The visitor would need to give the sponsor details of the firearm(s) and ammunition that he will possess while in the UK, and the reason for possessing them.
The Chief Officer of Police must be satisfied that they have good reason for having the firearms while they are in the United Kingdom, before they will issue a British Visitors Firearms Permit.
In scenario two, if you imports when resident in the UK, you will need to apply to the Chief Officer of Police for the area that you are resident in, for a UK Shotgun Certificate. You will need to state make, model and ammunition intended to be used on the application form, plus state where the shotgun will be stored when not in use.
Once you have obtained the shotgun certificate you can then import the shotgun against the Shotgun certificate that he had obtained.
Customs can detain firearms up to a period of three months; after that the firearm would be formally seized. If the importer thinks that it might take longer than the three-month period, it might be wise for the importer to get a Registered Firearms Dealer (RFD) to import and store the shotgun on their behalf, until he obtains the necessary shotgun certificate from the police.