The 47-year-old was beheaded by a British man who claims to be a member of the Islamic State.
The murder was recorded on film and uploaded online, but news outlets and search engines are refusing to allow it to be show on the Internet.
The aid worker from Salford was kidnapped on Boxing Day last year as he tried to deliver crucial aid to those affected by the Syrian civil war.
The brother of Alan’s wife, Barbara, spoke out on behalf of his distraught sister.
Mr Livesay told the BBC: “My heart's just sunk to a level that I never thought it could do.
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“I'm just devastated for my sister and two kids for what they've gone through, and it's so hard.
“We're all just saddened knowing that we've lost a great person in our family.
He added: “I just hope and pray they get what's coming to them. I've just so much hatred for them.”
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Before he was brutally murdered on videotape, Alan was filmed delivering a message to the UK government.
He said: “I am Alan Henning. Because of our parliament’s decision to attack the Islamic state I as a member of the British public will now pay the price for that decision.”
Channel 4 released footage taken of Alan Henning on Christmas Day 2013, just hours before he was kidnapped.
The video shows Alan looking cheerful as he takes a break from his important aid work. He speaks of his passion for helping people in Syria, despite missing out on Christmas celebrations with his family
Mr Henning is thr fourth hostage to be killed in recent months. British Aid worker David Haines has also been beheaded following the murder of American journalists Steven Sotloff and James Foley.