The first female bishop to take a seat in the House of Lords has said she would like a woman to be archbishop of Canterbury.

The Bishop of Gloucester, the Rt Rev Rachel Treweek, said "ideally" she would like a female to lead the world's Anglicans in the future.

Peers cheered and applauded as the Bishop took her seat in the House of Lords in a landmark moment for the Upper Chamber and the Church.

She was supported by the current Archbishop of Canterbury, Justin Welby, along with the Bishop of London, the Rt Rev Richard Chartres as she swore the oath of allegiance to the Queen.

Asked whether Lambeth Palace would be the next destination for a female member of the clergy, she told the Press Association: "I think the important thing is that the next archbishop of Canterbury is the right person.

"I ideally hope that one day there might be an archbishop of Canterbury who is also a woman. But I think what's most important is that it's always about the right person and being the person we have been called to be by God."

Bishop Treweek said the historical significance of her introduction to the Lords was "just beginning to sink in".

In an interview shortly before her introduction in the Upper Chamber she said: "I don't see myself as as a woman bishop, I see myself as a bishop who is a woman who is taking my place alongside other bishops who are men.

"I hope that what this is saying is that men and women are created equally. We work best when we are both able to use our voices alongside one another."

Asked how her approach would be different to male colleagues, she said: "What I bring is myself.

"First and foremost, I come here fully being myself and, as it happens, I'm a woman. It's quite a hard question, I think, generalisations about what do men do, what do women do.

"One thing I would say, I think women are good at doing connections, we are good at relating, I think we are good at doing big picture stuff.

"So I hope that one of the things I will do, at times I will be a bit challenging, to say 'how does that actually fit with this over here', how do we hold the big picture of human flourishing?"

She defended the role played within the House of Lords by the 26 Church of England bishops.

"There are people throughout the House of Lords of all faiths, that's very important to state that. As bishops I do think we bring something unique. We are connected with people across the whole spectrum of life.

"Every blade of grass, every inch of concrete in this country falls within one of the parishes in the Church of England. Therefore we are connecting with people's lives and can bring our voice here."

She said the bishops would welcome representatives of other faiths being given seats in the Lords.

Bishop Treweek added: "It's also important to remember that the Lords Spiritual are 26 voices amidst about 800 people. But am I keen that the Lords Spiritual keep their voice here, then yes, I most definitely am."

The Lord Speaker Baroness D'Souza said: "I am very happy to welcome Bishop Rachel to the House of Lords. Her introduction today is the culmination of 20 years' effort on the part of the Anglican Church and she will be a valuable addition to the Spiritual benches.

"Women make up more than a quarter of the membership of the House of Lords and the Leaders of both the Government and Opposition in the Lords are women. I am sure we will soon see Bishop Rachel become an active and effective contributor to the House's work. Her work will mean she can bring relevant experience to bear on many of the issues considered in the Lords."