Well the last time that I was in contact with the British Embassy in Washington DC, the estimated detention time prior to forced repatriation to the UK was between 6 and 12 weeks. Seemingly it takes some time for the Dep’t of Homeland Security to determine which further sanctions the detained person is to be subjected to, such as a lifetime ban for example.
You may also be interested to know that under American law there is simply no provision for appealing the decision of their Customs and Border Protection operatives through the law courts. The decision of CBP is final and binding.
My wife, an American citizen, refers to her country as certainly being the home of the brave, but the land of the free ? — well, that is debatable.