Taylor was jailed for 50 years in 2012 on 11 counts of war crimes and crimes against humanity over acts committed by Sierra Leonean rebels he aided and abetted during the brutal 1991-2001 civil war.
He was the first former head of state to be jailed by an international court -- the UN-backed Special Court for Sierra Leone in The Hague -- since the Nazi trials at Nuremberg in Germany after World War II.
Jones added: "The UK has a duty to ensure family life, not just for him but for his family. It's a clear duty under international law and English domestic law.
"If the UK is unable to make these family visits possible, no matter what he has been convicted of, he is going to serve a 50-year sentence, he has got a right to see his wife and children."
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"They took him to this prison where high (-risk) criminals, terrorists and other common British criminals are kept and he is being classified as a high-risk prisoner," his wife Victoria Addison Taylor told AFP last year.
"He is going through humiliation and you cannot treat a former head of state that way."
Britain's Foreign Office and Ministry of Justice did not immediately comment on the move.