I'm with you, gran. We have a sovereign power to refuse entry to anyone whose presence in our country is not in the public interest, as determined by the Secretary of State. This power may be exercised even after they've landed, but ought not to be exercised long after. If a man enters on false documents, I can't see that lapse of time stops him from being thrown out (That said, we have had cases of people who've been here for decades,without falsity, working and with children born here, who've been surprised to be told they are officially illegal!)
The underlying problem, which has been allowed to overrule anything else, existed before the Human Rights Act. We could not deport anyone, by extradition, if they were wanted by a foreign power and our court held that they would suffer cruel or unusual punishment or would not receive a truly fair trial. This, in effect is what has been allowed to happen here; the only country we can send him to is Jordan, and he'll be tried there if we send him
Best answer is to try him here on evidence we have; apparently not possible; or to let him free and wait until he commits an offence such as incitement to racial or religious hatred or murder