The footage will feature in Taking On The Tabloids, a documentary aired on Wednesday which follows Hugh Grant, who is fronting a "Hacked Off" campaign in the run up to the publication of Lord Leveson’s Report on his Inquiry.
Morgan has always claimed he knew phone hacking existed and maintains he never knowingly used it.
When he appeared before the Leveson Inquiry in December 2011, he was asked: "Have you listened to recordings of what you knew to be illegally obtained voicemail messages?"
Morgan replied: "I don't believe so, no."
Grant was given the never before seen footage and explains: “The other day at breakfast just before the Tory conference, we were chatting to Charlotte Church and she suddenly remembered that she had interviewed Piers Morgan for a speech she was making and it was videoed and in it he talked about phone hacking. So she has lent us the DVD and this it."
The exchange between Morgan and Church is as follows:
Morgan: "There was a spate of stories that came out because of mobile phones. When they first came out mobile phones journalists found out that if the celebrity hadn’t changed their pin code, right…"
Church: "Yeah, you can access their voicemail."
Morgan: "You can access, access their voicemail. Just by tapping in a number. Are you really telling me that journalists aren’t going to do that? If they know they can ring up Charlotte Church’s mobile phone, listen to all her messages…"
Church: "My God".
Morgan: "Right, now all you have to do and I know it’s hard because celebrities don’t like doing anything for themselves is actually change your security number."
Church: "Yeah, I’ve changed my security number".
Morgan: "And now you don’t have to worry".
In response to the programme, Morgan told The Guardian: "As I wrote in my book, The Insider, and as I reiterated at the Leveson inquiry, I was warned in 2001 about the practice of phone hacking, after a series of stories about me appeared in the press relating to a DTI share-tipping investigation and I couldn't work out where they had come from. I passed on that warning to others."
In May, Newsnight presenter Jeremy Paxman told the Leveson inquiry that Morgan had told him how to hack phones at a dinner in 2002.
Paxman said the former Daily Mirror editor was present at a dinner he attended at Mirror headquarters in Canary Wharf, where Morgan told him if you didn't change your default security code "you were in, his words, a fool".
The Leveson Inquiry was set up by Prime Minister David Cameron last July in response to revelations that the News of the World hacked murdered schoolgirl Milly Dowler's phone after she disappeared in 2002.