The move would mean that the Church would no longer have input into government and government could no longer involve itself in the running of the Church.
It would also see the Queen removed as the Supreme Governor of the Church.
Currently, archbishops and bishops are appointed by the Queen on the advice of the Prime Minister, who considers the names selected by a Church Commission. They take an oath of allegiance to The Queen on appointment and may not resign without Royal authority.
The connection between Church and State is also symbolised by the fact that the 'Lords Spiritual' (consisting of the Archbishops of Canterbury and York and 24 diocesan bishops) sit in the House of Lords. Parish priests also take an oath of allegiance to The Queen.
Nick Clegg believes the Anglican Church would 'benefit' from not being 'wrapped up' in the institutions of the state.
He also defended the Prime Minister's comments that Britain is a 'Christian country', saying it's time people simply 'acknowledged' that as a fact.
Roy Crown from HOPE UK, which helps churches to engage with their local communities, gave his reaction to Mr Clegg's comments on Premier's News Hour.
During an Easter reception at Lancaster House in London on Wednesday, Mr Clegg also praised the 'vital' role of the church in supporting those in need and creating 'human communities', with a special mention of the work they do with foodbanks.
He also garnered a few laughs by saying he wasn't planning for his speech to be nearly as controversial as the Prime Minister's pre-Easter comments had become a few days earlier.
Meanwhile, the Archbishop of Canterbury has hit back at athiests who criticised the Prime Minister in an open letter for labelling Britain as a "Christian country".
Writing in his blog, the Most Revd Justin Welby claims they were wrong to argue that expressing confidence in the country's Christian identity fosters alienation and division.
The letter, organised by the British Humanist Association and signed by over 50 public figures, including novelists, scientists, broadcasters, campaigners, authors, including authors Sir Terry Pratchett and Philip Pullman said: "We object to his characterisation of Britain as a 'Christian country' and the negative consequences for politics and society that this engenders."
Archbishop Justin countered their argument by pointing to the support Mr Cameron received from Muslim, Hindu and Sikh leaders on the issue.
He wrote: "Indeed, it is significant that non-Christian faith leaders, among them Anil Bhanot of the Hindu Council UK, Farooq Murad of the Muslim Council of Britain and Lord Indarjit Singh of the Network of Sikh Organisations, have spoken out in support of Mr Cameron.
"It is a historical fact (perhaps unwelcome to some, but true) that our main systems of ethics, the way we do law and justice, the values of society, how we decide what is fair, the protection of the poor, and most of the way we look at society . . . All have been shaped by and founded on Christianity.
"Add to that the foundation of many hospitals, the system of universal schooling, the presence of chaplains in prisons, and one could go on a long time. Then there is the literature, visual art, music and culture that have formed our understandings of beauty and worth since Anglo Saxon days.
"It is clear that, in the general sense of being founded in Christian faith, this is a Christian country. It is certainly not in terms of regular churchgoing, although altogether, across different denominations, some millions attend church services each week.
"Others of different backgrounds have also positively shaped our common heritage. But the language of what we are, what we care for and how we act is earthed in Christianity, and would remain so for many years even if the number of believers dropped out of sight (which they won't, in my opinion)."
The Deputy Prime Minister's post-Easter reception for Christian leaders was followed by a Easter egg hunt for school children who were also in attendance.