I am not legaly trained but you do have a right not to answer any questions put to you by a private person. Your contract of employment may specify what their security guards as agents can do, this however cannot break UK or EU law. Some other people than the police do have powers of arrest and caution, these are usually government or local authority officers. Do you work for a government or private organisation?.
If the security guard made you think that they were in some was connected to the police or that by not answering there questions you would be seen as guilty. Was it the whole British caution (like on The Bill or similar programmes), or a made up American one?.
Did you think you were arrested in any way and could not just leave if you wanted to. There could be a civil or criminal case. You could have a word with your Union, or any one who is in a union who also questioned. Try HR and tell then you are unhappy, somebody may have overstepped there powers and got carried away. I know that the Police are very hot on private companies trying to look like the police by vehicle marking, uniforms (thats why many wear American looking uniforms) as well as their actions and contact with the public. If you feel so strongly about it and get nowhere with internal complaints try your local Police.