JUSTIN Welby said there was every possible reason for optimism about the future of Christianity in the UK and worldwide as he was enthroned as the 105th Archbishop of Canterbury today.

The former Bishop of Durham was formally sworn in as the head of the Church of England and leader of the 77 million-strong worldwide Anglican Communion at Canterbury Cathedral in front of around 2,000 guests including the Prime Minister, Prince Charles and the Duchess of Cornwall and bishops from across the globe.

The 57-year-old succeeds Rowan Williams, who stood down late last year.

He was enthroned in a service which combined tradition and personal touches.

It began with Archbishop Welby banging on the Cathedral’s West Door and later he made an oath on the 1,500-year-old Canterbury Gospels.

The London-born old Etonian introduced a welcome greeting from a 17-year-old girl and was formally enthroned by the Venerable Sheila Watson, Archdeacon of Canterbury  - the first time a woman has performed the task.

Archbishop Welby used his sermon to challenge the church to step out of the “comfort” of traditions.

He praised the church for running food banks, sheltering the homeless, educating children, running debt counselling and comforting the bereaved.

But, in comments which will be taken as a warning to the Government, he also spoke up for the NHS and social care.

He said people “may properly differ” on the degrees of state and private responsibility in a healthy society but said challenges such as the environment, the economy, human development and poverty could only be faced with “Christ-liberated courage”.

Outside, dozens of people protested against public service cuts and the so-called Bedroom Tax.

Keith Woods, of Keep Our NHS Public, said it wasn’t a protest against Archbishop Welby as he had “been a supporter of what we are fighting for” but against David Cameron and the Government.

However, pro-gay campaigners carried banners directly criticising the church, for its attitude to homosexuality.

Earlier, it emerged the Archbishop had written to veteran campaigner Peter Tatchell offering face-to-face talks.

The invitation came after Mr Tatchell accused the Archbishop of being “homophobic”.

In his response, Archbishop Welby thanked Mr Tatchell for his “very thoughtful” letter and said the points he had made were “powerful”.

In a BBC News interview, the Archbishop said he backed traditional Church teaching on homosexuality but some gay relationships had “stunning quality” and he was “deeply challenged” by this.

In a separate Channel 5 interview, he said he believed there would be a female archbishop one day, despite the change having been rejected in a vote last November.

Pressed on the timing, he said: “Oh, I have no idea... when the right person turns up. But, yes, I think there certainly will.”

Security was tight as VIPs arrived at the cathedral. A 47-year-old man was arrested after allegedly running at a car carrying the Prince of Wales and the Duchess of Cornwall.

Eye witness Joel Tennant, 22, said police had to hold the man to the ground until the royal couple’s car passed by.

Earlier, Archbishop Welby had surprised media crews by running past the cathedral on an early morning jog, calling out “hello” as he passed at about 6.30am.