If a North Korean went to the UK Embassy in Pyongyang and requested an asylum, he would be politely asked to leave. If the person refuses to leave, the UK Embassy staff would call the North Korean police and ask them to remove the person from the premises.
If the person is a Christian who has been fleeing persecution, or she has any circumstances that would make the UK look bad for calling the police, they would just ignore the person. The Embassy would hope that this person would voluntarily leave the premises someday. This used to happen to the US embassy in the then Soviet Union.
Now let me tell you why the UK Embassy would do something like that. The reason is all the citizens from the Socialist countries needed to have an Exit Visa to leave the country. The Exit visa was issued by the Governments themselves. If you don’t have Exit Visa, you cannot leave the country, even if the UK or any other country issued you a Visa.
If a North Korean approached the UK Embassy in a different country, then the UK would consider your request.