Customs officers most certainly do have ID. From the HMRC Assistant Director of Criminal Investigation:
"We would always urge people to check the identification of those wanting to enter their home or business. Any legitimate law enforcement officer or caller will not mind waiting outside while their identity is verified. If you are suspicious, call the police."
Although Customs powers derive from the Police & Criminal Evidence Act, there are still certain activities only a policeman can perform.
I also seem to remember that the problem with landing sites in UK is not the permission to land but the permission to take off.
Phil